CN101320599A - Beam current continuous injection method through limit cycle helical sector injection section - Google Patents

Abstract

The invention discloses a continuous injection method of a beam current passing through a spiral fan-shaped section with a limit loop. A vacuum chamber is positioned in the gap between the upper magnetic pole and the lower magnetic pole of an axisymmetic dipole magnet. An upper pole surface and a lower pole surface are divided into the internal and external region by a particle balance orbit circle, at least one spiral fan-shaped section with the limit loop is inserted into one of the regions, wherein, the radial gradient index of the magnetic field is less than minus one for enabling the equation solution of particle motion to contain the limit loop which coincides with the arc segment of the balance orbit circle. The radial gradient index of the magnetic field in the neighboring spiral fan-shaped section is greater than or equal to minus one and less than zero, two radial gradient indexes constitutes one or more than one of the spiral fan-shaped period structure, the charged particle beam generated by an accelerator is directly injected into the stable area of the phase space of the circulating beam current at the balance orbit, thereby forming the collision fusion reactor of the continuous injection beam comprising the spiral fan-shaped section with the limit loop.

Description

The continuous method for implanting of line by the fan-shaped injection region of limit cycle spiral

One. technical field

The invention belongs to line impact fusion reactor field, be specifically related to a kind of continuous method for implanting of line by the fan-shaped injection region of limit cycle spiral.

Two. background technology

Huge in order to overcome Tokamak thermonuclear fusion reactor equipment, costed high shortcoming, people such as Rostoker have proposed a kind of line impact fusion reactor (Colliding Beam FusionReactor[CBFR]) [referring to N.Rostoker, et.al., Colliding Beam FusionReactor, Science, Vol.278,21 November (1997)].Promptly produce the low energy intense pulsed ion beam, be injected into the vacuum chamber that places between rotational symmetry dipolar magnet (or the superconduction magnetic mirror) air gap continuously, form annular circulation ion beam with accelerator.The magnetic field that the circulation ion beam produces strengthens with the strong accumulation of stream, its field intensity is during greater than main field, can operative constraint circulation ion beam self and plasma on every side, contrary plasma form of formation (Field-Reversed Configration[FRC]) [and referring to: N.Rostoker, et.al.PhysicalReview Letters Vol.20 Num.12 (1993) 1818].Therefore contrary plasma fusion reactor FRCR is otherwise known as.This technological approaches has clear superiority: the injected beam energy can accurately be controlled by accelerator, make circulation ion beam energy and the energy difference between the plasma on every side, remain on the resonance energy of reaction cross-section maximum and equate, significantly improve circulation ion beam and the plasma collision on every side probability that reacts, enlarged the scope that to use fusion fuel.Except that can be used to realize can be used for realizing the fusion of deuterium deuterium again the fusion of deuterium tritium deuterium helium-3 fusion and hydrogen boron-11 fusion.

Yet it is the serious technology barrier that line impact fusion reactor can't be crossed over that line injects continuously.A.N.Skrinsky says: " utilization does not rely on any external electromagnetic field of intrafascicular specified particle motion, can not make the line phase density obtain increasing.In this case, the line phase density of Tong Chang Suo Said is constant and determines that by initial condition (Liouville's theorem) always set up." [referring to: V.V.Parkhomchuk; A.N.Skrinsky; Reportson Preg.In Phys.Vol.54; No.7 (1991) 919] that is to say; according to the Liouville's theorem of phase space volume conservation, proving already that in theory line can not be injected in the constant electromagnetic field continuously, is impossible realize on the line impact fusion reactor theory; can't provide the technical design scheme, checking more can't experimentize.

Line can not be injected in the constant electromagnetic field continuously, not only is the technical barrier in line impact fusion reactor field; It also is the technical barrier in storage rings field.Disclosed application number is in State Intellectual Property Office: in " edge the focuses on the nonlinear damping storage rings " patent of " 00107730.9 ", proposed utilization " edge of two utmost point iron focuses on angle (7) greater than zero; the inlet limit of this two utmost points iron is parallel with the outlet limit; and equal zero in outlet edge focusing angle ", form storage rings with quadrupole electromagnet, beam level direction emittance is shunk, realize that line injects continuously.Owing to fail to break away from the restriction of Liouville's theorem, occur at dipolar magnet under the condition of edge focusing nonlinear damping, cause the quadrupole electromagnet nonlinear effect to cause the beam emittance expansion, both cancel out each other, beam emittance is still remained unchanged, just can not realize that also line injects continuously.Disclosed application number is in State Intellectual Property Office: in " the anti-Liouville's theorem heavy damping of the non-Hamiltonian's mechanical system charged particle storage rings " patent of " 02153963.4 ", propose to utilize " phase space volume is observed the anti-Liouville's theorem of constantly dwindling " " beam emittance can be shunk rapidly ", realize by " heavy damping charged particle storage rings ".Owing to fail to eliminate the instability of radial motion; Therefore, it is still unresolved to exist line not inject problem continuously in the storage rings.In addition, the edge that exists in storage rings focuses on and quadrupole electromagnet; In line impact fusion reactor, do not allow to occur, just more can not provide any technological borrowing yet for line impact fusion reactor.Line can not be injected in the constant electromagnetic field continuously, remains an insurmountable common technique difficult problem.

Yet it all is with good conditionsi that any theorem is set up, and Liouville's theorem is no exception.D.T.Greenwood says when the necessary condition that the explanation Liouville's theorem is set up: " the Jacobian determinant of putting corresponding canonical transformation does not mutually have zero point, just means that conversion mutually is corresponding one to one, and implying equation of motion uniqueness of solution yet." [referring to D.T.Greenwood, Classical Dynamics, (1977) P183] this shows, in solving the equation was unique constant electromagnetic field, promptly under the condition that Liouville's theorem is set up, line injected continuously and is impossible to realize; Otherwise in solving the equation was not unique constant electromagnetic field, Liouville's theorem was false, and just can thoroughly break away from the restriction of phase space volume conservation, and the particle beams can inject continuously along a certain special exercise track; Injected beam can form stabilizing ring stream along another special exercise track again continuously, injection efficiency is brought up near 100%, thereby can provide a practicable technical solution for line impact fusion reactor, for realizing the fusion of deuterium deuterium, deuterium helium-3 fusion and hydrogen boron-11 fusion etc., seek the easily new way of row of a simple economy, the problem to be solved in the present invention that Here it is.

Nominal definition:

[phase space] definition: given system of equations

$\frac{d{x}_i}{\mathrm{dt}}=f_i(t,x_1,x_2,L,x_n)$ (i＝1，2，L，n)

Claim (x ₁, x ₂, L, x _n) the space phase space of system of equations for this reason, when n=2, be called phase plane especially.When the system of equations right side functions does not show letter t, it separate curve as phase space, be called track.In other cases, solution curve often is called integrated curve.[referring to: " the mathematics handbook is write group, mathematics handbook, Higher Education Publishing House, (1979) 678]

[limit circle (or limit cycle)] definition: the situation that n=2 only is discussed here.

[periodic solution] definition: equation

$\frac{\mathrm{dx}}{\mathrm{dt}}=f_1(x,y)$

$\frac{\mathrm{dy}}{\mathrm{dt}}=f_2(x,y)$

The periodic solution that with T is the cycle is to satisfy x (t+T)=x (t), and y (t+T)=y (t) separates.The pairing track of periodic solution is a closed curve.Conversely, closed orbit is corresponding to periodic solution.

[limit circle (or limit cycle)]: isolated periodic solution is called equation [limit circle (or limit cycle)].Say that intactly exactly: establish x=x (t), y=y (t) is the periodic solution of equation, K is that this separates the closed curve of retouching out on phase plane.If there is positive number ρ, make for arbitrary and the some ξ of K distance on the phase plane less than ρ, equation cross a ξ just separate to be not the cycle, to claim x=x (t) so that y=y (t) (being closed orbit K) is isolated periodic solution, or [limit circle (or limit cycle)].[referring to: " the mathematics handbook is write group, mathematics handbook, Higher Education Publishing House, (1979) 685]

[equilibrium orbit] definition: in synchrotron, electronics is round a fixing track circumnutation, and this fixing track is the equilibrium orbit of accelerator.[referring to: Xu Jianming, accelerator principle, Science Press, (1974) 292]

Three. summary of the invention

1. the objective of the invention is to, a kind of continuous injecting method of line by the fan-shaped injection region of limit cycle spiral is provided.

The present invention is injected into the interior method of line impact fusion reactor vacuum chamber continuously to line.At the constant electromagnetic field dipolar magnet of rotational symmetry up and down between magnetic pole gap, be placed with the vacuum chamber that is used to realize the reaction of line impact fusion, the center of vacuum chamber overlaps with magnetic center, the central plane of vacuum chamber overlaps with the magnetic center face, it is characterized in that, the magnetic field vertical direction distributes and is divided into interior or outer two zones with the particle equilibrium orbit on the magnetic center face, one still keeps the magnetic field rotation of the classical cyclotron of Lao Lunsi to be symmetrically distributed, another zone is made up of the positive integer N 〉=1 fan-shaped periodic structure of a spiral, a fan-shaped injection region of limit cycle spiral is arranged in each periodic structure, the limit cycle in respective sector zone overlaps with the equilibrium orbit arc section, form two unit focusing system with the classical cyclotron spiral of the Lao Lunsi that does not have limit cycle fan section, charged particle beam by the accelerator generation, inject by outer rim line inlet, through limit cycle inside spin sector region, perhaps pass through limit cycle external spiral sector region, directly be injected in the line impact fusion reactor vacuum chamber inner equilibrium orbital cycle line phase space stabilized zone, injected beam can form stable circulation along closed equilibrium orbit in the vacuum chamber again continuously, form a line threeway zone, N 〉=1 thus, also form N 〉=1 a line inlet, main innovate point of the present invention that Here it is.

Satisfying the pole surface structure of above-mentioned specific magnetic fields distribution requirement can build in the following manner, in magnetic field along azimuth direction equally distributed magnetic mirror or classical cyclotron dipolar magnet up and down on the pole surface, additional N 〉=1 spirality parallels on the pole surface up and down in equilibrium orbit; Perhaps outside equilibrium orbit, be carved with N 〉=1 spiral groove on the pole surface up and down, form the corresponding spiral sector region that leads to limit cycle, and the selection limit ring just in time be the part of particle equilibrium orbit on the magnetic center plane; Vacuum chamber places dipolar magnet up and down between the pole surface, line by accelerator produces just can be injected by outer rim line inlet, through limit cycle inside spin sector region, perhaps, directly be injected in the equilibrium orbit circulation line phase space stabilized zone via limit cycle external spiral sector region; In vacuum chamber, fill, and form ionization under the bombardment repeatedly of stablizing circulation, form plasma and be subjected to directed circulation constraint and bombardment, just can realize line impact fusion reactor thus at injected beam with low density gas; Inject accumulation continuously with line and make and stablize that circulation stream is strong constantly to be strengthened, form the Luo Lunzili that constantly strengthens, can the operative constraint particle beams self and plasma medium on every side; When stream runs up to the condition of the Fu Lasuofu equation steady state solution that Rostoker obtains by force [referring to: N.Rostoker, et.al.Physical Review LettersVol.20 Num.12 (1993) 1818], just can realize a contrary field plasma form (FRC); The line injection efficiency utilizes the continuous injection efficiency of charge exchange line only to reach 6*10 near 100% with B.C.Maglich ^-6Compare [referring to: B.C.Maglich, Nucl.Instr.and Meth.In Phys.ResearchA271 (1988) 13], improved nearly 100,000 times, can effectively overcome the too low major defect of injection efficiency that the charge exchange method for implanting exists.Prove at first that below the necessary condition that limit cycle exists is that magnetic field radial gradient index n is less than negative 1; Then introduce the stability of particle movement, and four technical measures; Then be major parameter selection principle; Introduce the computer artificial result of embodiment and particle movement stability and injection efficiency at last.

2. there is the necessary condition of limit cycle in the particle movement equation in the stationary magnetic field

In cylindrical-coordinate system, do not exist under the time-independent condition in electric field and magnetic field, the equation of motion of charged particle [referring to: Xu Jianming, accelerator principle, Science Press, (1974) 92]:

$r^{\′\′}-r\·{\left({\mathrm{\θ}}^{\′}\right)}^2=\frac{e}{p}(r\·{\mathrm{\θ}}^{\′}\·B_z-z^{\′}\·B_{\mathrm{\θ}})$

$\frac{1}{r}\&CenterDot;\frac{d}{\mathrm{ds}}({\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\&CenterDot;{\mathrm{\&theta;}}^{\&prime;})=\frac{e}{p}(z^{\&prime;}\&CenterDot;B_r-r^{\&prime;}\&CenterDot;B_z)---\left(1\right)$

$z^{\&prime;\&prime;}=\frac{e}{p}(r^{\&prime;}\&CenterDot;B_{\mathrm{\&theta;}}-r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}\&CenterDot;B_r)$

$\sqrt{{\left(r^{\&prime;}\right)}^2+{(r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;})}^2+{\left(z^{\&prime;}\right)}^2}=1$

p＝m·γ·v

In the formula $\mathrm{\&gamma;}=\frac{1}{\sqrt{1-\frac{v^2}{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}}},$ Be commonly referred to relativity factor.In the stationary magnetic field that does not have electric field, motion particle rapidity modulus v is a constant, substitutes dt with the ds=vdt of arc length differential unit, and " r ' " expression respective amount r is to the difference quotient of arc length s in the formula; Except that special statement, the physical significance of other symbol is identical with usage.

The classical cyclotron rotational symmetry of Lao Lunzi main magnet, pole surface all is rotational symmetric up and down, azimuth direction component in magnetic field is zero on the magnetic center plane, that is: B _θ=0; When $z\&cong;z^{\&prime;}\&cong;0,$ And make B _z=-B (r), promptly the direction of axial field is just in time opposite with the sense of rotation of positively charged particle, and (1) formula becomes:

$r^{\&prime;\&prime;}=r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;2}-\frac{e}{p}\&CenterDot;r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}\&CenterDot;B\left(r\right)---\left(2\right)$

$\frac{1}{r}\&CenterDot;\frac{d}{\mathrm{ds}}({\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\&CenterDot;{\mathrm{\&theta;}}^{\&prime;})=\frac{e}{p}\&CenterDot;r^{\&prime;}\&CenterDot;B\left(r\right)$

$\sqrt{{\left(r^{\&prime;}\right)}^2+{(r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;})}^2}=1$

As everyone knows, first expression of following formula first formula right-hand member inertial centrifugal force; Second the Luo Lunzi centripetal force that the expression the action of a magnetic field produces, when both were equal, then particle was made circular motion, radius of circle r=r _eBe called equilibrium orbit radius.The first integral that is obtained the equation of motion by following formula second formula is:

$r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}=-\frac{e}{p}\&CenterDot;\frac{1}{r}{\&Integral;}_{r_i}^{r}r\&CenterDot;B\left(r\right)\&CenterDot;\mathrm{dr}+\frac{r_i^2\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}}{r}=-I\left(r\right)+\frac{r_i^2\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}}{r}---\left(3\right)$

$I\left(r\right)=\frac{e}{p}\&CenterDot;\frac{1}{r}{\&Integral;}_{r_i}^{r}r\&CenterDot;B\left(r\right)\&CenterDot;\mathrm{dr}$

$r^{\&prime;}=\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\&CenterDot;{\mathrm{\&theta;}}^{\&prime;2}}=\sqrt{1-{(I\left(r\right)-\frac{r_i^2\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}}{r})}^2}$

$\mathrm{V\&theta;}={\&Integral;}_{r_1}^{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}\frac{\mathrm{dr}}{\sqrt{1-{(I\left(r\right)-\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">r</figure-callout>}}_1^2\&CenterDot;{\mathrm{\&theta;}}_1^{\&prime;}}{r})}^2}}$

$\frac{e}{p}=\frac{1}{r_e\&CenterDot;B\left(r_e\right)}$

(3) formula is illustrated in the conservation of angular momentum of motion particle in the azimuth direction uniform magnetic field.

" mathematics rules " the 685th page about the ordinary differential equation limit cycle be defined as " isolated periodic solution is called (ordinary differential) equation limit cycle " [referring to: " the mathematics handbook is write group, the mathematics handbook, Higher Education Publishing House, (1979) 685], there is limit cycle in particle movement equation (2) on the magnetic center plane under a certain specified conditions, and these specified conditions can be obtained by (3) formula.In (3) formula first formula by r _iBe integrated to r _eThe time its value be under 1 the condition, that is:

$r_e\&CenterDot;{\mathrm{\&theta;}}_e^{\&prime;}=-I\left(r_e\right)+\frac{r_i^2\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}}{r_e}=-\frac{e}{p}\&CenterDot;\frac{1}{r_e}{\&Integral;}_{r_i}^{r_e}r\&CenterDot;B\left(r\right)\&CenterDot;\mathrm{dr}+\frac{r_i^2\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}}{r_e}=1---\left(4\right)$

By (3) formula the 3rd formula as can be known, its radial velocity r ' _e=0; And by (2) formula first formula as can be known, its radial acceleration r " _e=0, show from start radius r _iWith initial velocity r _iθ ' _iAnd r ' _iThe particle of incident all can arrive with r _eOn the equilibrium orbit for radius, with r _eFor the equilibrium orbit circle of radius is exactly the limit cycle of particle movement equation (2).Under these specified conditions, separating of particle movement equation (2) is not unique, constantly makes circular motion along the circulation bundle of particle that equilibrium orbit moves, from start radius r _i, with initial velocity r _iθ ' _iAnd r ' _iThe particle of incident can be injected into r through helical orbit _eOn the equilibrium orbit for radius, helical orbit can be expressed as the index curve equation

r＝a+b·e ^-θ/c (5)

Determine the particle movement orbital curve according to (4) formula, adopt least square method to try to achieve a in (5) formula, b, three constants of c are that line transits to r through the spiral sector region _eBe the theoretical foundation near the circulation bundle phase space stabilized zone equilibrium orbit of radius.

Can determine the radially-arranged particular requirement in magnetic field by the condition that satisfies (4) formula.Ds is multiply by at (2) formula first formula two ends, and integration gets:

$r_e^{\&prime;}-r_i^{\&prime;}={\&Integral;}_{r_i}^{r_e}(r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;2}-\frac{e}{p}\&CenterDot;r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}\&CenterDot;B\left(r\right))\frac{\mathrm{dr}}{r^{\&prime;}}---\left(6\right)$

As r ' _e=0 o'clock, with r _eBe only the limit cycle of the equation of motion (2) for the circle of radius.

At r _i＜r _eThe time, and as r '＞0, r ' _i, the minus necessary condition of (6) formula right-hand member integration to be at＞0 o'clock:

$(r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;2}-\frac{e}{p}\&CenterDot;r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}\&CenterDot;B\left(r\right))<0---\left(7\right)$

Otherwise, at r _i＞r _eThe time, and as r '＜0, r ' _i, (6) formula right-hand member integration to be equally at＜0 o'clock greater than zero necessary condition:

$(r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;2}-\frac{e}{p}\&CenterDot;r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}\&CenterDot;B\left(r\right))<0---\left(8\right)$

(7) (8) formula shows that (2) formula first formula right-hand member less than zero, illustrates inertial centrifugal force less than Luo Lunzi centripetal force, when particle by r _iFrom equilibrium orbit with interior incident, with initial velocity r ' _i＞0 and r _iθ ' _iTo with r _eFor the equilibrium orbit of radius near the time, radial velocity r ' _iModulus be subjected to radially decelerating effect and reduce, be met up to (4) formula, i.e. r _eθ ' _e=1, r ' _e=0; When particle by r _iFrom equilibrium orbit incident in addition, with initial velocity r ' _i＜0 and r _iθ ' _iTo with r _eFor the equilibrium orbit of radius near the time, radial velocity r ' _iModulus be subjected to radially decelerating effect and reduce, be met up to (4) formula, i.e. r _eθ ' _e=1, r ' _e=0.Illustrate that particle is by initial radium r _iAnd with initial velocity r ' _iAnd r _iθ ' _iTo with r _eDuring for the equilibrium orbit incident of radius, can transit on this equilibrium orbit, with r _eFor the circle of radius is the isolated periodic solution of the differential equation (2), be called the limit cycle of particle movement equation (2) again.

3. the instability of radial motion when radially linearization free oscillation equation and limit cycle exist

Make r=r _e+ x, x represents the particle radial position with respect to the departing from of equilibrium orbit in the formula, $\mathrm{d\&theta;}=\frac{\mathrm{ds}}{r},$ In substitution (2) formula, under first approximation [referring to: Xu Jianming, accelerator principle, Science Press, (1974) 368]:

$B\left(r\right)=B\left(r_e\right)[1+\frac{r_e}{B\left(r_e\right)}\&CenterDot;\frac{\mathrm{dB}\left(r\right)}{\mathrm{dr}}\&CenterDot;\frac{x}{r_e}]=B\left(r_e\right)[1+n\&CenterDot;\frac{x}{r_e}]$

$r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;2}-\frac{e}{p}\&CenterDot;r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}\&CenterDot;B\left(r\right)=\frac{1-r^{\&prime;2}}{r_e}(1-\frac{x}{r_e})-\frac{1}{r_e\&CenterDot;B\left(r_e\right)}\&CenterDot;\sqrt{1-r^{\&prime;2}}\&CenterDot;B\left(r_e\right)[1+n\&CenterDot;\frac{x}{r_e}]$

$r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;2}-\frac{e}{p}\&CenterDot;r\&CenterDot;{\mathrm{\&theta;}}^{\&prime;}\&CenterDot;B\left(r\right)=-\frac{1}{r_e}\&CenterDot;(1+n)\&CenterDot;\frac{x}{r_e}$

$n=\frac{r}{B\left(r\right)}\&CenterDot;\frac{\&PartialD;B\left(r\right)}{\&PartialD;r}<-1---\left(9\right)$

In the formula $n=\frac{r\&CenterDot;\&PartialD;B\left(r\right)}{B\left(r\right)\&CenterDot;\&PartialD;r},$ Be called axial magnetic field radial gradient index on the magnetic center plane, by the classical cyclotron theory and practice of Lao Lunzi experience as can be known, the necessary condition that satisfies (7) (8) formula is that the radial gradient index n in magnetic field is less than negative one.Hence one can see that, the necessary condition that particle is injected on the limit cycle is that magnetic field radial gradient index n must be less than negative 1, therefore select on the equilibrium orbit magnetic field gradient index n less than negative 1, just can realize that equilibrium orbit is exactly the limit cycle of particle movement equation, particle just can transit on the limit cycle.

As everyone knows, magnetic field radial gradient index n contradicts with the requirement of the cyclotron theory intermediate ion radial motion stability of Lao Lunzi classics just less than negative 1.The way that solves this contradiction is exactly both combinations, on pole surface about allusion quotation cyclotron two utmost point electromagnet of Lao Lunsi footpath, adds the spirality parallels on the pole surface up and down in equilibrium orbit; Perhaps outside equilibrium orbit, be carved with spiral groove on the pole surface up and down, form N 〉=1 a corresponding interior or external spiral sector region that leads to limit cycle, and the selection equilibrium orbit just in time be the limit cycle of particle movement equation on the magnetic center plane; Line by the accelerator generation, just can be by outer rim line inlet through equilibrium orbit limit cycle inside spin sector region, or via equilibrium orbit limit cycle external spiral sector region, directly be injected in the equilibrium orbit circulation line phase space stabilized zone, be called the continuous method for implanting of line through the fan-shaped injection region of limit cycle spiral, the device of making thus in order to realize the charged particle fusion reaction is called line impact fusion reactor.

4. the radial and axial linearization free oscillation equation of non-equilibrium particle movement and separating

Make r=r _e+ x, x represents the particle radial position with respect to the departing from of equilibrium orbit in the formula, $\mathrm{d\&theta;}=\frac{\mathrm{ds}}{r},$ In substitution (2) formula, under first approximation [referring to: Xu Jianming, accelerator principle, Science Press, (1974) 368]:

$\frac{d^2}{d{\mathrm{\&theta;}}^2}x+(1+n)\&CenterDot;x=0$

$\frac{d^2}{d{\mathrm{\&theta;}}^2}z-n\&CenterDot;z=0---\left(10\right)$

As everyone knows, grow in the classical cyclotron at Lao Lun, under the condition of magnetic field radial gradient index-1≤n 〉=0, particle movement is stable, but can not be injected in the equilibrium orbit phase space stabilized zone; As previously mentioned, under the condition of n≤-1, particle can be injected on the limit cycle, but radial motion is unsettled.Both combinations, pole surface is divided in interior or outer two zones with the particle equilibrium orbit up and down, one still keeps the classical cyclotron rotational symmetry structure of Lao Lunsi, and another zone is made up of the positive integer N 〉=1 fan-shaped periodic structure of a spiral, satisfies-1≤n in the magnetic field radial gradient _cUnder the condition of≤0 classical cyclotron, at 0≤θ _l≤ Δ θ _lA n is inserted in the interval, position angle _l≤-1 magnet, the cycle field structure of forming a similar spiral fan type isochronous cyclotron, the main difference of itself and spiral fan type isochronous cyclotron has three: one, and its structural cycle is counted N 〉=1: and be different from the spiral fan type isochronous cyclotron more than or equal to three N 〉=3: two, the fan-shaped periodic structure of spiral only is present in pole surface and is divided among the zone in interior or outer two zones with the particle equilibrium orbit; The 3rd, the magnetic field radial gradient have nothing in common with each other " referring to Xu Jianming, accelerator principle, Science Press, (1974) 224].Under the approximate condition of sharp boundaries, the particle movement equation also is the Hill equation, can directly use the notional result [referring to Xu Jianming, accelerator principle, Science Press, (1974) 369] of Courant and Snyder.At limit cycle spiral sector region interval 0≤θ _l≤ Δ θ _l, magnetic field radial gradient index n≤-1; In the formula $V{\mathrm{\&theta;}}_c+V{\mathrm{\&theta;}}_l=\frac{2\mathrm{\&pi;}}{N},$ N is the positive integer (N 〉=1) more than or equal to 1, is called magnetic pole periodic structure unit number.(10) the formula linear transfer matrix separated is [referring to Xu Jianming, accelerator principle, Science Press, (1974) 224]:

$M_{\mathrm{xl}}=\left(\begin{array}{cc}\mathrm{Ch}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">l</figure-callout>}}& \frac{1}{\sqrt{\left|n_l\right|-1}}\&CenterDot;\mathrm{Sh}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l\\ \sqrt{\left|n_l\right|-1}\&CenterDot;\mathrm{Sh}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l& \mathrm{Ch}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l\end{array}\right)$

$M_{\mathrm{zl}}=\left(\begin{array}{cc}\mathrm{Cos}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">l</figure-callout>}}& \frac{1}{\sqrt{\left|n_l\right|}}\&CenterDot;\mathrm{Sin}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l\\ -\sqrt{\left|n_l\right|}\&CenterDot;\mathrm{Sin}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l& \mathrm{Cos}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l\end{array}\right)---\left(11\right)$

In the classical cyclotron of Lao Lunsi interval $\mathrm{\&Delta;}{\mathrm{\&theta;}}_c=(\frac{2\&CenterDot;\mathrm{\&pi;}}{N}-\mathrm{\&Delta;}{\mathrm{\&theta;}}_l),$ Magnetic field radial gradient index-1≤n 〉=0; And limit the angular breadth Δ θ in limit cycle spiral sector region interval _l, smaller or equal to the angular breadth Δ θ in classical cyclotron interval _c, i.e. Δ θ _l≤ Δ θ _cIn classical cyclotron interval (is angular breadth Δ θ _cIn), the linear transfer matrix that corresponding (10) formula is separated is:

$M_{\mathrm{xc}}=\left(\begin{array}{cc}\mathrm{<figure-callout\; id="1"\; label="Cos"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Cos</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">c</figure-callout>}}& \frac{1}{\sqrt{1+n_c}}\&CenterDot;\mathrm{<figure-callout\; id="1"\; label="Sin"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Sin</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\\ -\sqrt{1+n_c}\&CenterDot;\mathrm{<figure-callout\; id="1"\; label="Sin"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Sin</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="c\; Cos"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">c</figure-callout>}}& \mathrm{Cos}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\end{array}\right)$

$M_{\mathrm{zc}}=\left(\begin{array}{cc}\mathrm{Cos}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">c</figure-callout>}}& \frac{1}{\sqrt{\left|n_c\right|}}\&CenterDot;\mathrm{Sin}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\\ -\sqrt{\left|n_c\right|}\&CenterDot;\mathrm{Sin}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c& \mathrm{Cos}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\end{array}\right)---\left(12\right)$

The transmission matrix of one-period is:

M _x＝M _xc·M _xl

M _z＝M _zc·M _zl (13)

5. the stability of radial and axial linearization free oscillation particle movement

The expression formula that can be obtained judging particle movement stability by (13) formula is [referring to Xu Jianming, accelerator principle, Science Press, (1974) 372]:

$\mathrm{Cos}{\mathrm{\&mu;}}_x=\frac{M_{x11}+M_{x22}}{2}$

$\mathrm{Cos}{\mathrm{\&mu;}}_z=\frac{M_{z11}+M_{z22}}{2}---\left(14\right)$

μ in the formula _xAnd μ _zRepresent that respectively particle is every through one-period, the phase angle change amount of radial oscillation and axial oscillation [referring to: Xu Jianming, accelerator principle, Science Press, (1974) 381], the condition of particle movement stability is:

Cosμ _x≤1

Cosμ _z≤1 (15)

(14) expression formula of respective transmissions matrix element is in the formula:

$M_{x11}=\mathrm{<figure-callout\; id="1"\; label="Cos"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Cos</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Ch}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l+\frac{\sqrt{\left|n_l\right|-1}}{\sqrt{1+n_c}}\&CenterDot;\mathrm{<figure-callout\; id="1"\; label="Sin"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Sin</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Sh}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l$

$M_{x22}=\mathrm{<figure-callout\; id="1"\; label="Cos"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Cos</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Ch}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l-\frac{\sqrt{1+n_c}}{\sqrt{\left|n_l\right|-1}}\&CenterDot;\mathrm{<figure-callout\; id="1"\; label="Sin"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Sin</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Sh}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l$

$M_{z11}=\mathrm{Cos}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Cos}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l-\frac{\sqrt{\left|n_l\right|}}{\sqrt{\left|n_c\right|}}\&CenterDot;\mathrm{Sin}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Sin}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l$

$M_{z22}=\mathrm{Cos}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Cos}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l-\frac{\sqrt{\left|n_c\right|}}{\sqrt{\left|n_l\right|}}\&CenterDot;\mathrm{Sin}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Sin}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l---\left(16\right)$

Substitution (14) and (15) formula get:

$\mathrm{<figure-callout\; id="1"\; label="Cos"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Cos</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Ch}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l-\frac{1}{2}\&CenterDot;\frac{\sqrt{1+n_c}\&CenterDot;\sqrt{\left|n_l\right|-1}}{\left(\right|n_l|-1)\&CenterDot;(1+n_c)}\&CenterDot;\left(\right|n_l|-n_c-2)\&CenterDot;$

$\mathrm{<figure-callout\; id="1"\; label="Sin"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">Sin</figure-callout>}\sqrt{1+n_c}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Sh}\sqrt{\left|n_l\right|-1}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l\&le;1---\left(17\right)$

$\mathrm{Cos}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Cos}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l-\frac{1}{2}\&CenterDot;\frac{\sqrt{\left|n_l\right|}\&CenterDot;\sqrt{\left|n_c\right|}}{n_l\&CenterDot;n_c}\&CenterDot;(n_l+n_c)\&CenterDot;\mathrm{Sin}\sqrt{\left|n_c\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_c\&CenterDot;\mathrm{Sin}\sqrt{\left|n_l\right|}\mathrm{\&Delta;}{\mathrm{\&theta;}}_l\&le;1$

Be compiled into the Sect1.for calculation procedure according to last two formulas.According to [referring to: Xu Jianming, accelerator principle, Science Press, (1974) 374] Fig. 7-12, the stability range in the synoptic diagram of stable region, but initial option parameter, n _cWith (| n _l|-1) modulus should be between 0.2 to 0.3, and then do checking computations and improve by numerical evaluation.Line covers line can adopt Courant and Snyder[referring to Xu Jianming, accelerator principle, Science Press, (1974) 375] identical method tries to achieve.

6. four technical measures

Four technical measures: the one, adopt classical cyclotron rotational symmetry dipolar magnet of Lao Lunsi or superconduction magnetic mirror, magnetic field radial gradient index-1≤n 〉=0.The 2nd, determine equilibrium orbit radius r _e, under the condition that changes along the azimuth direction cycle in magnetic field, equilibrium orbit radius r _eBe the mean value of the instantaneous radius-of-curvature of closed cycle equilibrium orbit.The 3rd, with mean equilibrium orbit radius r _eFor the circumference of radius is divided into inside and outside two zones to pole surface, one still keeps the classical cyclotron rotational symmetry structure of Lao Lunsi, and another zone is divided into a spiral fan section, N 〉=1 along azimuth direction; In the structural cycle of N in equilibrium orbit 〉=1, add the spirality parallels up and down on the pole surface; Perhaps outside equilibrium orbit, in the structural cycle of N 〉=1, be carved with spiral groove on the pole surface up and down, form and correspondingly lead in the limit cycle or the external spiral sector region, and to select equilibrium orbit just in time be the limit cycle of particle movement equation on the magnetic center plane.The 4th, because limit cycle spiral sector region magnetic field radial gradient index n is less than negative 1, allusion quotation cyclotron two utmost point electromagnet intervals, Lao Lunsi footpath, magnetic field radial gradient index-1≤n 〉=0 just in time can require make compensation according to alternating-gradient focusing.These four technical measures combinations both can guarantee with the magnetic center to be the stability of the radial and axial motion of annular circulating particle in the center of circle; Can make again particle by outer rim line inlet through equilibrium orbit limit cycle inside spin sector region, or, directly be injected in the equilibrium orbit circulation line phase space stabilized zone via equilibrium orbit limit cycle external spiral sector region.

Four. embodiment and embodiment

Inject continuously as embodiment with single channel limit cycle inside spin fan section line, promptly N=1 does to specify the present invention.

On pole surface about allusion quotation cyclotron two utmost point electromagnet of Lao Lunsi footpath, in equilibrium orbit, add the spirality parallels on the pole surface up and down, form the corresponding inside spin sector region that leads to limit cycle, and the selection limit ring just in time is the part of particle movement equation equilibrium orbit on the magnetic center plane, is called the continuous method for implanting of line of the fan-shaped injection region of limit cycle inside spin.Inject continuously as embodiment with the fan-shaped injection region of single channel N=1 limit cycle inside spin line below, do to specify.As building system physical engineerings such as charged particle accelerator or fusion reactor, all to implement according to the following step:

The one, physical Design: according to the purpose that will realize, determine the main magnet main physical parameters,, just can determine magnetic field intensity, equilibrium orbit radius as injecting certain specific charged particle and particular energy.Select equilibrium orbit radius as the limit cycle radius,, calculate the incident condition of injecting continuously by the fan-shaped injection region of limit cycle inside spin line according to (3) formula:

$r_i\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}=\frac{r_e}{r_i}\&CenterDot;[1-\frac{1}{r_e\&CenterDot;B\left(r_e\right)}\&CenterDot;\frac{1}{r_e}\underset{r_i}{\overset{r_e}{\&Integral;}}r\&CenterDot;B\left(r\right)\&CenterDot;\mathrm{dr}]---\left(18\right)$

$r_i^{\&prime;}=\sqrt{1-{(r_i\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;})}^2}$

Utilize the field distribution function, call Simpson's integration external function, at initial radium r _i, r _eAfter determining, can try to achieve the starting condition r ' that reaches the limit of the ring particle by (18) formula _i, r _iθ ' _iThen; Utilize Long Ge-Kao Ta method that (2) formula is found the solution, can be in the hope of reaching the limit of ring particle movement track and phase path; Make main field reverse, perhaps make Long Ge-Kao Ta method calculate step-length for negative, counter pushing away satisfied the incident condition r ' that reaches the limit of ring spiral sector region porch _i, r _iθ ' _iRequirement, can be in the hope of the starting condition r ' at equilibrium orbit external beam current inlet place _Int, r _Intθ ' _IntThe absorbing boundary equation that reaches the limit of ring spiral sector region also can be found the solution definite by Long Ge-Kao Ta method to (2) formula, and determines the shape of additional spirality parallels thus.Using the same method can analogue simulation charging particle movement process.Computer software RCPSSP (Reactor of Charged Particles withSpiral Sector Passage) can finish these functions.

Main magnet can be according to the conventional method design-build, can write " Numerical Calculation of Electromagnetic Fields and electromagnet design " referring to Li Quanfeng, the 164th page, " design of cyclotron electromagnet " carried out [referring to Li Quanfeng, Numerical Calculation of Electromagnetic Fields and electromagnet design, publishing house of Tsing-Hua University, (2002) 164].

The 2nd, the design of overall plan and engineering-built according to the purpose that will realize, is done well-designedly to each subsystem, forms a complete system design scheme, remakes engineering-built design.Each subsystem, as vacuum, forceful electric power, light current, computer control, experimental monitoring, water is cool, ventilates, and safety interlockings etc. all can carry out design-build according to conventional method according to the purpose that will realize, the debugging of subsystem installation and processing, last total the accent.

The 3rd, particle movement stability and injection efficiency computer artificial result.

Use the RCPSSP program, differential equation group (1) is carried out numerical solution, calculating step-length step=0.01, nh=10 ⁵The time, when promptly step-length being got ten thousand/millimeter, error calculated is less than 0.01mm, identical with reality processing and installation accuracy, thereby accurate simulation particle motion process in line impact fusion reactor, people are referred to as Computer Simulation usually, can obtain the reliable design sketch of the present invention.

The fan-shaped injection region of limit cycle inside spin line being injected continuously after embodiment made general description, described in detail by accompanying drawing more below.

Five. Figure of description

Fig. 1. rotational symmetry main magnet structure planing surface figure.

Fig. 2. the fan-shaped injection region of limit cycle spiral magnet pole-face structure vertical view.

Fig. 3. the radial distribution figure that enters the court in magnetic center plane, the fan-shaped injection region of limit cycle inside spin.

Fig. 4. the vacuum chamber structure vertical view.

Fig. 5. particle is by the outer particle movement track computer artificial result that is injected into equilibrium orbit through limit cycle inside spin fan section of equilibrium orbit.

Fig. 6. the particle of corresponding figures 5 is by the outer phase path that is injected into equilibrium orbit through limit cycle inside spin fan section of equilibrium orbit.

Fig. 7. injected beam particle levels direction incident angle departs from+the particle movement phase path of 10 milliradians.

Fig. 8. injected beam particle levels direction incident angle departs from the particle movement phase path of-10 milliradians.

Fig. 9. injected beam particle levels direction incident radial position departs from+10 millimeters particle movement phase path.

Figure 10. injected beam particle levels direction incident radial position departs from-10 millimeters particle movement phase path.

Figure 11. injected beam particle movement in vertical direction track.0.01 meter of curve incident vertical coordinate position, top, speed are zero; Lower curve incident vertical coordinate position zero, speed is 10 milliradians.

Figure 12. injected beam particle movement in vertical direction track.0.01 meter of curve incident vertical coordinate position, top, speed are zero; Lower curve incident vertical coordinate is zero, and speed is-10 milliradians.

Six. description of drawings

Fig. 1 axial symmetry main magnet structure planing surface figure is to inject continuously the line collision by limit cycle spiral fan shaped district The fusion reactor main body. 1 is upper magnetic pole among the figure, the 2nd, and lower magnetic pole, the 3rd, go through magnetic coil, the 4th, yoke can According to the conventional method design-build, and can [write " Numerical Calculation of Electromagnetic Fields and Electromagnetic Design " with reference to Li Quanfeng, The 164th page, " cyclotron Electromagnetic Design "]. The fan-shaped injection region of limit cycle inside spin is injected line continuously The measure of impact fusion reactor unique technology is lower magnetic pole on allusion quotation cyclotron two utmost point electromagnet of Lao Lunsi footpath On the face, magnetic pole strength adds the spirality parallels up and down in equilibrium orbit; Perhaps at the outside upper lower magnetic pole of equilibrium orbit Be carved with spiral groove on the face, form the corresponding interior or external spiral sector region that leads to limit cycle, and select balance Track just in time is the limit cycle of Particles Moving equation on the magnetic center plane; Require to do according to alternating-gradient focusing simultaneously Go out compensation. So, lead in the spiral fan shaped district scope of limit cycle magnetic field gradient index corresponding N can realize that less than bearing 1 equilibrium orbit also is the limit cycle of spiral fan shaped district Particles Moving equation; Corresponding Lead to beyond the spiral fan shaped regional extent of limit cycle, at the alternating-gradient focusing compensatory zone, still resemble Lao Lunsi The same in the allusion quotation cyclotron of footpath, magnetic field gradient index n keeps greater than negative 1 and less than zero, simultaneously can Reach the stability of circulation Shu Yundong.

Fig. 2 is limit cycle inside spin fan section continuous injection magnet pole-face structure top view, and 1 expression is from the center line of the initial helix parallels of pole center among the figure, and two borders of spiral parallels apart from the angular breadth of this center line are

$\frac{V{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">l</figure-callout>}}}{2}+\frac{V{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">c</figure-callout>}}}{2}=\&PlusMinus;\frac{\mathrm{\&pi;}}{N},$ N 〉=1 is positive integer. 2 cylindrical represents the outward flange of magnetic pole among the figure, inner edge arrow 2 The limit cycle in the circle expression spiral fan shaped district that indication is littler, its radius should be got and make equilibrium orbit radius r_e At figure In on the corresponding spirality parallels between lower magnetic pole air gap increase with radius, make magnetic field gradient index less than Bear 1, can realize that line transits to equilibrium orbit circulation bundle through limit cycle inside spin sector region radius porch In the phase space stability region. So, approximate lower in sharp boundaries, at limit cycle inside spin sector region $\mathrm{V\&theta;}=\&PlusMinus;\frac{{\mathrm{V\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">l</figure-callout>}}}{2}$ The interval, the distribution B (r) in magnetic field can be expressed as the piecewise continuous function of a single variable of radius r on the magnetic center face:

$B\left(r\right)=B\left(r_e\right)\&CenterDot;[1+\frac{r}{B\left(r\right)}\&CenterDot;\frac{\&PartialD;B\left(r\right)}{\&PartialD;r}\&CenterDot;\frac{r_e-r}{r_e}]$ 0≤r≤r ₁    (19)

B(r)＝B(r _c)·[1+vr] ${\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">r</figure-callout>}}_1<r\&le;{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">r</figure-callout>}}_2;[{\mathrm{\&theta;}}_l\left(r\right)-\frac{V{\mathrm{\&theta;}}_l}{2}]\&le;\mathrm{\&theta;}\&le;[{\mathrm{\&theta;}}_l\left(r\right)+\frac{V{\mathrm{\&theta;}}_l}{2}]$

$\mathrm{vr}=\mathrm{Amplt}\&CenterDot;(\cos (\mathrm{\&pi;}\&CenterDot;\frac{r-r_1}{r_2-r_1})-\cos (\mathrm{\&pi;}\&CenterDot;\frac{r_e-r_1}{r_2-r_1}))$

$\mathrm{Amplt}=\frac{\mathrm{<figure-callout\; id="1"\; label="br"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">br</figure-callout>}1}{1-\cos (\mathrm{\&pi;}\&CenterDot;\frac{r_e-r_1}{r_2-r_1})}$

$B\left(r\right)=B\left(r_e\right)\&CenterDot;[1+\frac{r}{B_d\left(r\right)}\&CenterDot;\frac{\&PartialD;B_d\left(r\right)}{\&PartialD;r}\&CenterDot;\frac{r_e-r}{r_e}]$ ${\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20071011042400202.png,A20071011042400222.png"\; state="\{\{state\}\}">r</figure-callout>}}_1<r\&le;{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20071011042400211.png"\; state="\{\{state\}\}">r</figure-callout>}}_2,[{\mathrm{\&theta;}}_l\left(r\right)-\frac{\mathrm{\&pi;}}{N}]\&le;\mathrm{\&theta;}\&le;\left[({\mathrm{\&theta;}}_l\left(r\right)-\frac{V{\mathrm{\&theta;}}_l}{2})\right]$

With $[{\mathrm{\&theta;}}_l\left(r\right)+\frac{V{\mathrm{\&theta;}}_l}{2}]\&le;\mathrm{\&theta;}\&le;\left[({\mathrm{\&theta;}}_l\left(r\right)+\frac{\mathrm{\&pi;}}{N})\right]$

$B\left(r\right)=B\left(r_e\right)\&CenterDot;[1+\frac{r}{B\left(r\right)}\&CenterDot;\frac{\&PartialD;B\left(r\right)}{\&PartialD;r}\&CenterDot;\frac{r_e-r}{r_e}]$ r ₂＜r≤r ₃

Following formula represents that the Distribution of Magnetic Field function radially is divided into Three regions, at 0≤r≤r₁The center, and r₂＜r≤r ₃ The outer radius interval, with similar in the allusion quotation cyclotron of footpath, magnetic field gradient index n keeps greater than negative 1 and little In zero; At r₁＜r≤r ₂Middle radius interval, Distribution of Magnetic Field function are to change in the cycle along azimuth direction, $[{\mathrm{\&theta;}}_l\left(r\right)-\frac{V{\mathrm{\&theta;}}_l}{2}]\&le;\mathrm{\&theta;}\&le;[{\mathrm{\&theta;}}_l\left(r\right)+\frac{V{\mathrm{\&theta;}}_l}{2}]$ Limit cycle inside spin sector region interval, $[{\mathrm{\&theta;}}_l\left(r\right)-\frac{\mathrm{\&pi;}}{N}]\&le;\mathrm{\&theta;}\&le;\left[({\mathrm{\&theta;}}_l\left(r\right)-\frac{V{\mathrm{\&theta;}}_l}{2})\right]$ With $[{\mathrm{\&theta;}}_l\left(r\right)+\frac{V{\mathrm{\&theta;}}_l}{2}]\&le;\mathrm{\&theta;}\&le;\left[({\mathrm{\&theta;}}_l\left(r\right)+\frac{\mathrm{\&pi;}}{N})\right]$ Be allusion quotation cyclotron interval, footpath, the angular breadth of one-period is: $\frac{2\mathrm{\&pi;}}{N}=V{\mathrm{\&theta;}}_l+V{\mathrm{\&theta;}}_c,$ N represents the structural cycle number in magnetic field in the formula. Zone outside the spiral fan shaped zone among the figure, $[{\mathrm{\&theta;}}_l\left(r\right)-\frac{\mathrm{\&pi;}}{N}]\&le;\mathrm{\&theta;}\&le;\left[({\mathrm{\&theta;}}_l\left(r\right)-\frac{V{\mathrm{\&theta;}}_l}{2})\right]$ With $[{\mathrm{\&theta;}}_l\left(r\right)+\frac{V{\mathrm{\&theta;}}_l}{2}]\&le;\mathrm{\&theta;}\&le;\left[({\mathrm{\&theta;}}_l\left(r\right)+\frac{\mathrm{\&pi;}}{N})\right],$ Magnetic field gradient index is that alternating-gradient focusing is mended greater than bearing 1 Repay the district, the two unit of both corresponding compositions condenser lens, the stability of assurance Particles Moving.

Fig. 3 is the radial distribution figure in the fan-shaped injection zone of limit cycle inside spin magnetic field, and corresponding mathematic(al) representation is (19) formula. Transverse axis represents the particle radial position, and unit is rice; The longitudinal axis represents the distribution in magnetic field on the magnetic center face Function B (r), unit are tesla. 1 expression r=r among the figure₁Radial position, at r≤r₁The time, central plane It is uniform entering the court; 2 expression r=r among the figure_eRadial position, be exactly the limit cycle radial position; 3 tables among the figure Show r=r₂Radial position, at r₁＜r≤r _eEntering the court in interval, central plane is fast-descending, can guarantee r=r_eThe time field gradient index n_e(17) formula stability requirement is satisfied in 〉=(1.3); 4 expression r=r among the figure₃Radial position, at r≤r₃The time, it is slow decreasing that central plane is entered the court, and accelerates with the allusion quotation convolution of Lao Lunsi footpath The distribution of device midfield is similar. The distribution curve in this magnetic field satisfies to go out from magnetic center with maximum radial speed r '=1 The particle of penetrating all can reach the limit of ring, is convenient to determine the start radius r of spiral parallels≤r₁ Compile with reference to Li Quan wind Work " Numerical Calculation of Electromagnetic Fields and Electromagnetic Design ", the 164th page, " cyclotron Electromagnetic Design " [ginseng See: Li Quanfeng, Numerical Calculation of Electromagnetic Fields and Electromagnetic Design, publishing house of Tsing-Hua University, (2002) 164], According to the distribution curve in this magnetic field, can determine the Luo Kaofusi base curves of spiral parallels curved surface.

Fig. 4 is the vacuum chamber structure vertical view, the interface of 1 expression vacuum chamber and beam transport pipeline among the figure, and the circular vacuum chamber sidewall of 2 expressions is an annulus among the figure; The vacuum chamber planing surface is a square frame; Vacuum chamber places on Fig. 1 main magnet between the pole surface 1 and lower magnetic pole face 2, for the particle beams and plasma provide living space, adopts sealing or open vacuum structure, creates one and is lower than 10 ^-6The mm Hg high vacuum condition is to reduce circulation line and air molecule collision causing scattering loss.The particle beams by injector produces enters vacuum chamber through conveying pipe along the horizontal direction of arrow 1, in limit cycle inside spin sector region porch transits to equilibrium orbit circulation bundle phase space stabilized zone.

Fig. 5 is that particle is by the outer computer artificial result that is injected into the limit cycle track through limit cycle inside spin sector region of equilibrium orbit.In cartesian coordinate system, the unit of the transverse axis longitudinal axis is a rice.Make main field reverse, perhaps make Long Ge-Kao Ta method calculate step-length for negative, can be in the hope of by outside the equilibrium orbit, via corresponding incident condition of leading to the inside spin sector region of limit cycle.Initial radial position of particle and azimuth direction position are injected in 1 expression of curve starting point arrow.The line of injector generation, be transported to outside the equilibrium orbit by direction shown in Fig. 4 arrow 1, satisfy the incident condition of leading to limit cycle inside spin sector region via corresponding, after this corresponding particle movement track injected beam inflow entrance shown in the arrow 1 from Fig. 5 that is injected into equilibrium orbit is initial, approximately just arrive on the equilibrium orbit circumference through most circles, this certain tracks is called incident equilibrium particle track; The place of injected beam inflow entrance shown in the arrow 1 is about 120mm to the circle spacing between the equilibrium orbit among Fig. 5, and much larger than the injected beam beamwidth, the line of can avoiding circulating strikes and causes unnecessary loss on the cutting plate.

Fig. 6 is that particle is by the outer phase path that is injected into limit cycle through limit cycle inside spin sector region of equilibrium orbit.In cartesian coordinate system, transverse axis represents that the particle radial position is offset equilibrium orbit, and unit is a rice; The longitudinal axis is represented radial velocity, and unit is a radian.Initial radial position offset of particle and initial radial velocity are injected in 1 expression of curve starting point arrow.The vacuum that directly is added to indoor circulation line phase space range of stability was restrainted in the phase space stabilized zone in circulation near particle transitted to equilibrium orbit by external radius phase space reference position.The terminal of curve is a small circle among the figure, rather than x=0, and the desirable point of x '=0 illustrates that the point in the Computer Simulation is different from geometric point.

Fig. 7 is the particle movement phase path that injected beam particle levels direction incident angle departs from incident equilibrium particle+10 milliradians.In cartesian coordinate system, transverse axis represents that the particle radial position is offset equilibrium orbit, and unit is a rice; The longitudinal axis is represented radial velocity, and unit is a radian.Initial radial position offset of particle and initial radial velocity are injected in 1 expression of curve starting point arrow.The vacuum that directly is added to indoor circulation line phase space range of stability was restrainted in the phase space stabilized zone in circulation near particle transitted to equilibrium orbit by external radius phase space reference position.

Fig. 8 is the particle movement phase path that injected beam particle levels direction incident angle departs from incident equilibrium particle (10) milliradian.In cartesian coordinate system, transverse axis represents that the particle radial position is offset equilibrium orbit, and unit is a rice; The longitudinal axis is represented radial velocity, and unit is a radian.Initial radial position offset of particle and initial radial velocity are injected in 1 expression of curve starting point arrow.The vacuum chamber circulation line phase space that directly is added to range of stability was restrainted in the phase space stabilized zone in circulation near particle transitted to equilibrium orbit by external radius phase space reference position.

Fig. 9 is the particle movement phase path that injected beam particle levels direction incident radial position departs from incident equilibrium particle+10 millimeter.In cartesian coordinate system, transverse axis represents that the particle radial position is offset equilibrium orbit, and unit is a rice; The longitudinal axis is represented radial velocity, and unit is a radian.Distance and the initial radial velocity that the initial radial position of particle departs from equilibrium orbit injected in 1 expression of curve starting point arrow.The vacuum chamber circulation line phase space that directly is added to range of stability was restrainted in the phase space stabilized zone in circulation near particle transitted to equilibrium orbit by external radius phase space reference position.

Figure 10 is the particle movement phase path that injected beam particle levels direction incident radial position departs from incident equilibrium particle (10) millimeter.In cartesian coordinate system, transverse axis represents that the particle radial position is offset equilibrium orbit, and unit is a rice; The longitudinal axis is represented radial velocity, and unit is a radian.Distance and the initial radial velocity that the initial radial position of particle departs from equilibrium orbit injected in 1 expression of curve starting point arrow.The vacuum chamber circulation line phase space that directly is added to range of stability was restrainted in the phase space stabilized zone in circulation near particle transitted to equilibrium orbit by external radius phase space reference position.

Fig. 6 shows to the result of Figure 10, is not the particle that a certain specific incident condition is only arranged, and just can be injected near the circulation bundle of the equilibrium orbit phase space stabilized zone; But the particle beams with certain emittance, circulation is restrainted in the phase space stabilized zone near all can being injected into equilibrium orbit, Fig. 6 incoming beam horizontal direction emittance in Figure 10 is 400mm mrad, (millimeter milliradian), the reception degree of illustrative system produces the emittance of line much larger than at present general injector, line by the accelerator generation, can be by outer rim through equilibrium orbit limit cycle inside spin sector region, directly be injected in the equilibrium orbit circulation line phase space stabilized zone, injection efficiency is 100% in theory, and actual conditions should be approaching with computer artificial result.

Figure 11 is an injected beam particle movement in vertical direction track.Transverse axis is represented radial position, and Z-axis is represented the vertical direction position, and unit all is a rice.Right-hand member is the initiating terminal of two movement locus among the figure, and the initial radial position of injection particle is identical with the incident condition of Fig. 5 porch with the azimuth direction position, 0.01 meter of top curve incident vertical coordinate position, and speed is zero; Lower curve incident vertical coordinate position zero, speed is 10 milliradians, be injected near the equilibrium orbit after, particle is done around the magnetic center plane freely to shake, amplitude is about 0.02 meter, illustrates that movement in vertical direction is stable.

Figure 12 is an injected beam particle movement in vertical direction track.Transverse axis is represented radial position, and Z-axis is represented the vertical direction position, and unit all is a rice.Right-hand member is the initiating terminal of two movement locus among the figure, and the initial radial position of injection particle is identical with the incident condition of Fig. 5 porch with the azimuth direction position, 0.01 meter of top curve incident vertical coordinate position, and speed is zero; Lower curve incident vertical coordinate is zero, and speed be-10 milliradians, be injected near the equilibrium orbit after, particle freely shakes around magnetic center plane work, amplitude is about 0.01 meter, illustrates that movement in vertical direction is stable.

In this embodiment, there is not the field of rising in radial field, and the particle movement in vertical direction can not be subjected to any debunching force effect, and theoretical similar fully with experimental result to Lao Lunsi footpath allusion quotation cyclotron, the particle movement in vertical direction is stable.

Figure 11 shows to the result of Figure 12, is not the particle that a certain specific incident condition is only arranged, and just can be injected near the circulation bundle of the equilibrium orbit phase space stabilized zone; But the particle beams with certain emittance, circulation is restrainted in the phase space stabilized zone near all can being injected into equilibrium orbit, Figure 11 incoming beam vertical direction emittance in Figure 12 is 400mm mrad, (millimeter milliradian), the reception degree of illustrative system produces the emittance of line much larger than at present general injector, line by the accelerator generation, can be by outer rim through equilibrium orbit limit cycle inside spin sector region, directly be injected in the equilibrium orbit circulation line phase space stabilized zone, injection efficiency is 100% in theory, and actual conditions should be approaching with computer artificial result.

As B.C.Maglich [referring to B.C.Maglich, Nucl.Instr.and Meth.InPhys.ResearchA271 (1988) 13], in vacuum chamber, fill under the condition with certain rare book gas, stand the bombardment of vacuum chamber circulation line repeatedly and ionization, form plasma, and be subjected to constraint of vacuum indoor circulation line labor Lenze power and the bombardment of circulation line, realize the nuclear reaction of line impact fusion.

Seven. the invention effect

The present invention proposes a kind of by the continuous method for implanting of limit cycle spiral fan shaped district line, the result shows, the serious restriction of phase space volume conservation Liouville's theorem is thoroughly broken away from this invention, line is injected in the equilibrium orbit circulation beam phase space stability region continuously via the spiral fan shaped zone that leads to limit cycle, obtains following positive effect:

The one, line inlet place shown in arrow 1 in the accompanying drawing 5 is about to the circle spacing between the equilibrium orbit 120mm, much larger than the injected beam beamwidth, the line of can avoiding circulating strikes and causes unnecessary damage on the cutting plate Consumption.

The 2nd, the injection efficiency height is shown in accompanying drawing 6 to 12, because system equipment horizontal direction and vertical direction The reception degree is much larger than the incident beam emittance, and 100% injection efficiency is to realize easily. With the B.C.Maglich electricity Lotus exchange 610^-6Injection efficiency is compared [referring to B.C.Maglich, Nucl.Instr.and Meth.In Phys.ResearchA271 (1988) 13], improved nearly 100,000 times.

The 3rd, line is injected by outer rim line inlet place, through limit cycle inside spin sector region, perhaps passes through Limit cycle external spiral sector region is directly injected into line impact fusion reactor vacuum chamber inner equilibrium orbital cycle In the beam phase space stability region, injected beam can form stabilizing ring along closed equilibrium orbit in the vacuum chamber again continuously Stream forms a line threeway zone, N 〉=1 thus, also forms N shown in arrow 1 in the accompanying drawing 5 〉=1 line Inlet.

The 4th, simple economy is easily gone, and line is injected into the circulation line continuously via leading to limit cycle spiral fan shaped zone In the phase space stability region, need not plus external beam current cooling device, need not additional additional investment. For realizing heat Nuclear fusion provides a new way that reality is feasible.

The 5th, applied range, the image charge exchange is injected, and is to the inapplicable inherent defect of electron beam, also just natural Eliminated, it both had been applicable to electron beam, also was applicable to cation, anion, and various charge state ion beams, Enlarged the scope that to use fusion fuel. Except can be used to realize the fusion of deuterium tritium, can be used for again realizing that the deuterium deuterium is poly-Become deuterium helium-3 fusion and hydrogen boron-11 fusion.

The 6th, it is wide to be suitable for energy range, low energy beam, and high energy beam all is suitable for, and is especially concerning low energy beam, respectively existing It is all inapplicable to plant the line cooling means, and also just not having available beam stream to inject accumulation method can use, and the present invention then becomes The realization low energy beam is injected the alternative unique channel of accumulation continuously.

The 7th, can form the stable circulation take pole center as orbit centre, produce corresponding Lao Luncili, can have Plasma and line self around the effect constraint make line reach more high brightness, make plasma reach highly denser Degree.

The 8th, provide the easily new way of row of a simple economy for realizing contrary plasma (FRC) steady state. Run up under the condition of megampere level at the stable circulation take magnetic center as orbit centre, can be with its operative constraint Plasma forms a stable inversion field plasma (FRC) form [referring to N.Rostoker, et.al.Physical Review Letters, Vol.20 Num.12 (1993) 1818].

Claims (5)

1. continuous method for implanting of line by the fan-shaped injection region of limit cycle spiral, at the constant electromagnetic field dipolar magnet of rotational symmetry up and down between magnetic pole gap, be placed with the vacuum chamber that is used to realize the reaction of line impact fusion, the center of vacuum chamber overlaps with magnetic center, the central plane of vacuum chamber overlaps with the magnetic center face, it is characterized in that, the magnetic field vertical direction distributes and is divided into interior or outer two zones with the particle equilibrium orbit on the magnetic center face, one still keeps the magnetic field rotation of the classical cyclotron of Lao Lunsi to be symmetrically distributed, another zone is made up of the positive integer N 〉=1 fan-shaped periodic structure of a spiral, a fan-shaped injection region of limit cycle spiral is arranged in each periodic structure, the limit cycle in respective sector zone overlaps with the equilibrium orbit arc section, form two unit focusing system with the classical cyclotron spiral of the Lao Lunsi that does not have limit cycle fan section, charged particle beam by the accelerator generation, shown in arrow 1 in the Figure of description 5, inject by the line inlet of outer rim shown in arrow among Fig. 51, through limit cycle inside spin sector region, perhaps pass through limit cycle external spiral sector region, directly be injected in the line impact fusion reactor vacuum chamber inner equilibrium orbital cycle line phase space stabilized zone, injected beam can form stable circulation along closed equilibrium orbit in the vacuum chamber again continuously, form a line threeway zone, N 〉=1 thus, also form the N 〉=1 line inlet shown in arrow among Fig. 51.Make thus in order to realize the device of thermonuclear fusion reaction, be called continuous injection line impact fusion reactor with limit cycle spiral fan section.

2. pass through the continuous method for implanting of line in limit cycle spiral fan section according to claim 1, satisfying the pole surface structure of above-mentioned specific magnetic fields distribution requirement can build in the following manner, in magnetic field along azimuth direction equally distributed magnetic mirror or classical cyclotron dipolar magnet up and down on the pole surface, additional N 〉=1 spirality parallels on the pole surface up and down in equilibrium orbit; Perhaps outside equilibrium orbit, be carved with N 〉=1 spiral groove on the pole surface up and down, form the corresponding spiral sector region that leads to limit cycle, and the selection limit ring just in time be the part of particle equilibrium orbit on the magnetic center plane.

3. pass through the continuous method for implanting of line in limit cycle spiral fan section according to claim 1, be divided in inside and outside two zones with particle equilibrium orbit circle at pole surface up and down, one of them has and is no less than a fan-shaped injection region of limit cycle spiral, wherein radial gradient index in magnetic field is less than negative 1, and satisfies following integral relation

$r_e\&CenterDot;{\mathrm{\&theta;}}_e^{\&prime;}=-I\left(r_e\right)+\frac{r_i^2\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}}{r_e}=-\frac{e}{p}\&CenterDot;\frac{1}{r_e}{\&Integral;}_{r_i}^{r_e}r\&CenterDot;B\left(r\right)\&CenterDot;\mathrm{dr}+\frac{r_i^2\&CenterDot;{\mathrm{\&theta;}}_i^{\&prime;}}{r_e}=1---\left(1\right)$

Spiral fan section center line is expressed as the index curve equation

r＝a+b·e ^-θ/c (2)

Determine particle movement helical orbit curve according to (1) formula, adopt least square method to try to achieve a in (2) formula, b, three constants of c, make that there is limit cycle in the particle movement equation in this fan section, and overlap with the equilibrium orbit arc section, as above among Fig. 5 shown in the arrow 1, the particle of specific incident condition can be injected on the equilibrium orbit continuously by limit cycle spiral fan section.

4. pass through the continuous method for implanting of line in limit cycle spiral fan section according to claim 1, the classical cyclotron of the Lao Lunsi that in each periodic structure, faces mutually zone with limit cycle spiral fan section, magnetic field radial gradient index is more than or equal to negative 1 and less than zero, there is not limit cycle in this zone, form N 〉=1 two unit focusing system with limit cycle spiral fan section, and satisfy following stability condition

$\mathrm{Cos}\sqrt{1+n_c}{\mathrm{\&Delta;\&theta;}}_c\&CenterDot;\mathrm{Ch}\sqrt{\left|n_l\right|-1}{\mathrm{\&Delta;\&theta;}}_l-\frac{1}{2}\&CenterDot;\frac{\sqrt{1+n_c}\&CenterDot;\sqrt{\left|n_l\right|-1}}{\left(\right|n_l|-1)\&CenterDot;(1+n_c)}\&CenterDot;\left(\right|n_l|-n_c-2)\&CenterDot;$

$\mathrm{Sin}\sqrt{1+n_c}{\mathrm{\&Delta;\&theta;}}_c\&CenterDot;\mathrm{Sh}\sqrt{\left|n_l\right|-1}{\mathrm{\&Delta;\&theta;}}_l\&le;1---\left(3\right)$

$\mathrm{Cos}\sqrt{\left|n_c\right|}{\mathrm{\&Delta;\&theta;}}_c\&CenterDot;\mathrm{Cos}\sqrt{\left|n_l\right|}{\mathrm{\&Delta;\&theta;}}_l-\frac{1}{2}\&CenterDot;\frac{\sqrt{\left|n_l\right|}\&CenterDot;\sqrt{\left|n_c\right|}}{n_l\&CenterDot;n_c}\&CenterDot;(n_l+n_c)\&CenterDot;\mathrm{Sin}\sqrt{\left|n_c\right|}{\mathrm{\&Delta;\&theta;}}_c\&CenterDot;\mathrm{Sin}\sqrt{\left|n_l\right|}{\mathrm{\&Delta;\&theta;}}_l\&le;1$

Guarantee the stability of particle beams horizontal direction and movement in vertical direction, make the emittance of the beam acceptance of equipment greater than injected beam.

5. pass through the continuous method for implanting of line in limit cycle spiral fan section according to claim 1, shown in 5 to 12 design sketch in the Figure of description, the reception degree of horizontal direction and vertical direction, all greater than the emittance of injected beam, injected beam forms stable circulation circulation continuously, in the vacuum chamber plasma under the constraint of stable circulation circulation labor human relations magnetic force and the line that is subjected to circulating bombard repeatedly, make in order to realize the device of thermonuclear fusion reaction, be called continuous injection line impact fusion reactor with limit cycle spiral fan section.

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