CN114360842A - Light periodic magnetic field coil applied to high-power microwave source - Google Patents

Light periodic magnetic field coil applied to high-power microwave source Download PDF

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CN114360842A
CN114360842A CN202111629002.3A CN202111629002A CN114360842A CN 114360842 A CN114360842 A CN 114360842A CN 202111629002 A CN202111629002 A CN 202111629002A CN 114360842 A CN114360842 A CN 114360842A
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magnetic field
electron beam
solenoids
power microwave
microwave source
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CN114360842B (en
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王海涛
杨超超
崔言程
朱丹妮
袁玉章
谢明亮
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Naval University of Engineering PLA
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F5/00—Coils
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
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Abstract

The invention discloses a light periodic magnetic field coil applied to a high-power microwave source, wherein the high-power microwave source comprises a radial transit time oscillator, the periodic magnetic field coil comprises a plurality of sections of excitation coils which are uniformly arranged on the outer wall of a beam interaction region of the radial transit time oscillator at intervals, each excitation coil comprises a plurality of layers of densely wound solenoids which are oppositely arranged on two sides of the outer wall of the beam interaction region, a plurality of solenoids which are positioned on the same side of the beam interaction region are linearly arranged, and an insulator is arranged between two adjacent solenoids which are positioned on the same side of the outer wall of the beam interaction region; the superposed magnetic field B (r) generated in the electron beam channel of the beam wave interaction area after the solenoids are electrified is in cosine distribution; wherein the peak value B of the superimposed magnetic field0Is the Brillouin magnetic field B of the electron beam under the corrected relativistic conditionbIs/are as follows
Figure DDA0003439449830000011
The magnetic field parameter alpha of the superimposed magnetic field B (r) is 0-0.66 or 1.72-3.76. The invention can reduce the weight of the external magnetic field coil on the premise of ensuring the stable transmission of radial strong current relativistic electron beams.

Description

Light periodic magnetic field coil applied to high-power microwave source
Technical Field
The invention belongs to the field of vacuum electronics, and particularly relates to a lightweight periodic magnetic field coil applied to a high-power microwave source.
Background
The high-power microwave technology refers to the technology of generation, transmission, measurement, application and the like of electromagnetic waves with the output power of 100MW to 100GW and the frequency of 100MHz to 100 GHz. High power microwave sources generate microwaves by energy exchange between a high current relativistic electron beam and an eigenmode field in a high frequency structure. The microwave source is the core of a high-power microwave system, the front stage of the microwave source is a pulse driving source, and the rear stage of the microwave source is a mode conversion and radiation antenna. High power microwaves have many applications, such as directed energy, electron countermeasure, and plasma heating. To meet the application requirements in these fields, the miniaturization of devices is a research focus.
In a radial transit-time oscillator, a strong current relativistic electron beam forms density clusters under the synchronous action of a high-frequency field. With the continuous increase of the cluster, the space charge density of the clustered electron beams is also continuously increased, the space charge repulsive force is continuously enhanced, in addition, the space repulsive force among electrons is superposed, the transmission of the electron beams becomes disordered and disordered, the electrons bombard the metal surface to cause radio frequency breakdown to generate plasma, the energy exchange with an intrinsic mode field is influenced, and further, the working efficiency of the device is reduced.
An external guidance magnetic field is generally used to generate a focusing force, focus and guide the high current relativistic electron beam. The magnetic field is generally uniform, and is formed by generating induction magnetic fields by a plurality of excitation coils with equal size and extruding the induction magnetic fields mutually in space. In fact, the structure of the field coil leaves much room for improvement if only for the purpose of directing the electron beam.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a light periodic magnetic field coil applied to a high-power microwave source, which reduces the weight of an external magnetic field coil and meets the requirements of light and small devices on the premise of ensuring the stable transmission of radial strong current relativistic electron beams.
In order to achieve the above object, the present invention provides a light-weight periodic magnetic field coil applied to a high power microwave source, wherein the high power microwave source comprises a radial transit time oscillator, the light-weight periodic magnetic field coil comprises a plurality of sections of excitation coils uniformly arranged on the outer wall of a beam interaction region of the radial transit time oscillator at intervals, each excitation coil comprises a plurality of layers of densely wound solenoids arranged on two sides of the outer wall of the beam interaction region, a plurality of solenoids arranged on the same side of the beam interaction region are arranged in a straight line, and an insulator is arranged between two adjacent solenoids arranged on the same side of the outer wall of the beam interaction region;
the superposed magnetic field B (r) generated in the electron beam channel of the beam wave interaction area after the solenoids are electrified is distributed in a cosine way; wherein a peak value B of the superimposed magnetic field0Is the Brillouin magnetic field B of the electron beam under the corrected relativistic conditionbIs/are as follows
Figure BDA0003439449810000021
The magnetic field parameter alpha of the superposed magnetic field B (r) is 0-0.66 or 1.72-3.76.
Compared with the traditional guide magnetic field coil adopting uniformly and densely wound excitation coils, the light periodic magnetic field coil applied to the high-power microwave source provided by the invention adopts a plurality of sections of excitation coils which are uniformly arranged at intervals, each excitation coil comprises a plurality of layers of densely wound solenoids which are oppositely arranged on two sides of the outer wall of the beam wave interaction region of the radial transit time oscillator, and an insulator is arranged between two adjacent solenoids on the same side of the outer wall of the beam wave interaction region, so that the whole and the whole of the whole and small-diameter magnetic field coils are arranged in a compact mode, and can be used in a small-diameter mode, and can be used for the whole field coilThe weight of each coil; simultaneously, the position and the peak value B of the superposed magnetic field generated after the solenoids are electrified are regulated and controlled0And a magnetic field parameter alpha, which can reduce the fluctuation of the electron beam and ensure the stable transmission of the electron beam in the electron channel.
In one embodiment, the Brillouin magnetic field BbThe calculation formula of (2) is as follows:
Figure BDA0003439449810000031
brillouin magnetic field B of electron beam under the relativistic conditionbThe formula for calculating the correction coefficient k is:
Figure BDA0003439449810000032
in the formula I0Represents the current flowing into the diode in the radial transit time oscillator, and the unit is A; u represents the voltage across a diode in a radial transit time oscillator; a represents the radius of the electron beam generated by the diode in the radial transit time oscillator, in mm; epsilon0Represents the vacuum dielectric constant; eta0Represents the charge-to-mass ratio of electrons in kV; gamma represents a factor of relativity and gamma represents,
Figure BDA0003439449810000033
m0representing the resting mass, m the relativistic mass, c the speed of light, and e the elementary charge.
In one embodiment, the magnetic field parameter α is calculated by the formula:
Figure BDA0003439449810000034
in the formula, L represents the length of a single solenoid.
In one embodiment, the period length z of the superimposed magnetic field b (r) is calculated according to the trajectory equation of the edge electrons of the electron beam under the relativistic condition, where the trajectory equation of the edge electrons of the electron beam under the relativistic condition is:
Figure BDA0003439449810000035
wherein R represents the normalized beam radius of the electron beam,
Figure BDA0003439449810000036
r represents the electron beam radius; r is0Represents the cosine mean radius of the electron beam; beta represents a space charge parameter of the electron beam,
Figure BDA0003439449810000037
in one embodiment, two adjacent solenoids on the same side are supplied with currents with the same magnitude and the same direction, and two oppositely arranged solenoids are supplied with currents with the same magnitude and the opposite directions, so that the superposed magnetic field b (r) generated by each solenoid in the electron beam channel of the beam interaction region is in cosine distribution.
In one embodiment, the supply current I of each solenoid is set according to configuration parameters of each solenoid, and the calculation formula of the supply current I is as follows:
Figure BDA0003439449810000041
in the formula, a superposed magnetic field
Figure BDA0003439449810000042
j represents the current density in the case of continuous current distribution, j equals NI/[2L [0(R2-R1)]；R1、R2Correspondingly representing the inner and outer radius of each solenoid; 2L of0Represents half of the total length of the solenoid; n represents the total number of turns of the solenoid.
In one embodiment, the configuration parameters of each solenoid are set accordingly according to the size of the beam interaction region of the radial time-of-flight oscillator.
In one embodiment, each solenoid is wound by copper-core enameled wires with the diameter of 4 mm.
In one embodiment, the insulator is made of insulating bakelite.
Drawings
FIG. 1 is a diagram of the fluctuation of an electron beam under the action of a periodic cosine magnetic field;
FIG. 2 is a graph of the distribution of a lightweight periodic magnetic field coil on a radial time-of-flight oscillator provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of the arrangement of solenoids within a lightweight periodic magnetic field coil in accordance with an embodiment of the present invention;
FIG. 4 is a graph of the superimposed magnetic field distribution in an embodiment of the present invention;
FIG. 5 is a diagram illustrating the transmission of electron beams within electron channels in accordance with one embodiment of the present invention;
FIG. 6 is a graph of microwave output power in accordance with an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order to solve the problem that the weight of a guide magnetic field coil applied to a radial transit time oscillator is heavy, the invention provides a light periodic magnetic field coil applied to a high-power microwave source, which can reduce the weight of the coil and meet the requirements of light and small devices on the premise of ensuring the stable transmission of radial strong current relativistic electron beams in an electronic channel in the radial transit time oscillator.
It should be noted that, by adding a guidance magnetic field coil to the radial transit time oscillator to ensure stable transmission of the electron beam under the strong current relativistic condition, the following conditions need to be satisfied:
(1) the guiding magnetic field coil is in a non-immersion focusing mode (the magnetic field at the electron emission surface is zero);
(2) the magnetic field generated by the guidance field coil satisfies a cosine distribution, i.e.
Figure BDA0003439449810000051
(B0Peak magnetic flux density, z is cycle length);
(3) a radial space-charge-free electric field;
(4) the magnetic field generated by the guidance field coil is uniform across all electron beam cross-sections.
The working principle of ensuring stable transmission of electron beams by adding the guidance field coil is as follows: the periodic cosine magnetic field generated by the guiding magnetic field coil exerts a strong convergent force on the electron beam, and the force can not only counteract the divergent force of space charge, but also enable the electron to obtain a radial acceleration. As shown in fig. 1, the electrons change from off-axis motion in the absence of a magnetic field to on-axis motion about the radial centerline. When the converging force of the magnetic field is too small to counteract the diverging force of the space charge, the electrons become moved off-axis again until the next period of the strong magnetic field is entered. It follows that the electrons move from time to the axis during this process, and vice versa, i.e. there is a fluctuation in the envelope of the electron beam, which is allowed during the beam wave interaction.
Fig. 2 is a schematic structural diagram of a lightweight periodic magnetic field coil applied to a high power microwave source according to an embodiment of the present invention, and as can be seen from fig. 2, the lightweight periodic magnetic field coil applied to a high power microwave source according to the present invention includes a plurality of excitation coils 100 uniformly spaced apart from each other and disposed on an outer wall of a beam interaction region of a radial transit time oscillator. In this embodiment, the multiple excitation coils 100 are disposed on the outer wall of the beam wave interaction region of the radial transit time oscillator, so that the superimposed magnetic field generated after the multiple excitation coils 100 are energized acts on the electron channel of the beam wave interaction region, and the magnetic field intensity at the end face of the electron beam emitted from the cathode of the diode in the radial transit time oscillator is negligible compared with the magnetic field intensity in the beam wave interaction region, that is, the magnetic field intensity at the end face of the electron beam is equivalent to zero, thereby ensuring that the electron beam satisfies the above-mentioned condition (1) for stable transmission.
Each of the excitation coils 100 provided in this embodiment includes a plurality of layers of tightly wound solenoids disposed opposite to each other on both sides of the outer wall of the beam interaction region, a plurality of solenoids disposed on the same side of the beam interaction region are linearly arranged, and an insulator is disposed between two adjacent solenoids disposed on the same side of the outer wall of the beam interaction region. Compared with the traditional excitation coil which adopts uniform and dense winding, the embodiment symmetrically arranges the plurality of solenoids which are uniformly arranged at intervals at two sides of the outer wall of the beam wave interaction area, and can ensure that the superposed magnetic field generated after each solenoid is electrified is uniform in the cross section of all electron beams, thereby ensuring that the electron beams meet the stable transmission condition (4); the two excitation coils are separated by adopting the spaced excitation coils, the insulator is arranged between the two adjacent excitation coils and can be made of insulating materials such as insulating bakelite and the like, and the requirement of reducing the weight of the field coil can be realized on the basis of ensuring the stable transmission of electron beams emitted by a cathode of a diode in the radial transit time oscillator.
To ensure that the guiding magnetic field coil provided in this embodiment has the same focusing effect on the electron beam as the conventional coil using uniform magnetic field, the superimposed magnetic field B (r) generated in the electron beam channel in the beam wave interaction region after the solenoids are energized provided in this embodiment needs to be distributed in cosine, and the peak value B of the superimposed magnetic field is similar to that of the periodic permanent magnet system0Is the Brillouin magnetic field B of the electron beam under the corrected relativistic conditionbIs/are as follows
Figure BDA0003439449810000071
Double, i.e.
Figure BDA0003439449810000072
Thereby ensuring that the electron beam satisfies the above-described condition (2) for stable transmission.
Wherein the Brillouin magnetic field Bb(magnitude of uniform magnetic field for balancing electron beam):
Figure BDA0003439449810000073
brillouin magnetic field B of electron beam under relativistic conditionsbCorrection coefficient k of (a):
Figure BDA0003439449810000074
in the formula I0Represents the current flowing into the diode in the radial transit time oscillator, and the unit is A; u represents the voltage across a diode in a radial transit time oscillator; a represents the radius of the electron beam generated by the diode in the radial transit time oscillator, in mm; epsilon0Represents the vacuum dielectric constant; eta0Represents the charge-to-mass ratio of electrons in kV; gamma represents a factor of relativity and gamma represents,
Figure BDA0003439449810000075
m0representing the resting mass, m the relativistic mass, c the speed of light, and e the elementary charge.
And because the stability of the electron beam is related to the magnetic field parameter α of the superimposed magnetic field b (r), in order to ensure the stability of the electron beam, according to the marginal electron trajectory equation of the electron beam under the relativistic condition, when the value of the magnetic field parameter α of the superimposed magnetic field b (r) is between 0 and 0.66 or between 1.72 and 3.76, the space charge divergence force of the electron beam can be counteracted, thereby ensuring that the electron beam satisfies the above-mentioned condition (3) of stable transmission. Preferably, the value of the magnetic field parameter α of the superimposed magnetic field b (r) lies between 0 and 0.66, in which case the required magnetic field strength of the superimposed magnetic field b (r) is minimal.
In the non-immersion focusing mode, the trajectory equation of the edge electrons of the electron beam under the condition of strong current relativity can be simplified as follows:
Figure BDA0003439449810000081
wherein the magnetic field parameter
Figure BDA0003439449810000082
z represents the period of the superimposed magnetic field B (r)The length of the period; l represents the length of a single solenoid; r represents the normalized beam radius of the electron beam,
Figure BDA0003439449810000083
r represents the electron beam radius; r is0Represents the cosine mean radius of the electron beam; beta represents a space charge parameter of the electron beam,
Figure BDA0003439449810000084
the trajectory equation is a nonlinear differential equation with a periodic coefficient, belongs to a slit equation, and has the characteristic that the solution is possibly stable and also possibly unstable, the stability of the electron beam is related to the magnitude of a magnetic field parameter alpha, and the stability of the electron beam is difficult to maintain in an unstable area; in the first stabilization zone, the value of the magnetic field parameter α lies between 0 and 0.66; in the second stabilization zone, the value of the magnetic field variable α lies between 1.72 and 3.76. Preferably, the electron beam is most suitably focused in the first stable region, where the required magnetic field strength is minimal.
Compared with the traditional guiding magnetic field coil which adopts uniformly densely wound excitation coils, the light periodic magnetic field coil applied to the high-power microwave source provided by the embodiment adopts multiple sections of excitation coils which are uniformly arranged at intervals, each excitation coil comprises multiple layers of densely wound solenoids which are oppositely arranged on two sides of the outer wall of the beam wave interaction region of the radial transit time oscillator, and an insulator is arranged between two adjacent solenoids on the same side of the outer wall of the beam wave interaction region, so that the weight of the whole coil can be effectively reduced; simultaneously, the position and the peak value B of the superposed magnetic field generated after the solenoids are electrified are regulated and controlled0And a magnetic field parameter alpha, which can reduce the fluctuation of the electron beam and ensure the stable transmission of the electron beam in the electron channel.
In one embodiment, in order to make the superimposed magnetic fields b (r) generated by the solenoids in the electron beam passage of the beam interaction region in a cosine distribution, two solenoids adjacent to each other on the same side are supplied with current with the same magnitude and the same direction, two solenoids opposite to each other are supplied with current with the same magnitude and the opposite directions, so that the directions of the magnetic fields generated by two solenoids adjacent to each other on the same side at the position of the electron beam passage of the beam interaction region are opposite, and the directions of the magnetic fields generated by two solenoids opposite to each other at the position of the electron beam passage of the beam interaction region are the same, so that the superimposed magnetic fields b (r) at the position of the electron beam passage of the whole beam interaction region are in a cosine distribution.
Specifically, the supply current I of each solenoid can be set according to the configuration parameters of each solenoid, and the calculation formula of the supply current I is as follows:
Figure BDA0003439449810000091
in the formula, the superimposed magnetic field B (r) is a peak value B obtained by the above calculation0And period z is determined, i.e.
Figure BDA0003439449810000092
j represents the current density in the case of continuous current distribution, j equals NI/[2L [0(R2-R1)]；R1、R2Correspondingly representing the inner and outer radius of each solenoid; 2L of0Represents half of the total length of the solenoid; n represents the total number of turns of the solenoid.
Wherein, the configuration parameter (R) of each solenoid in the formula1、R2N, L) can be set correspondingly according to the size of the beam wave interaction area of the radial transit time oscillator, and after the configuration parameters of each solenoid are determined, the power supply current I of each solenoid can be determined.
The following description will be made by taking an example that the lightweight periodic magnetic field coil provided by the present invention focuses an electron beam in a Ku-band radial transit time oscillator:
the radial transit time oscillator of the Ku waveband is composed of a diode, a four-gap modulation cavity, a two-gap extraction cavity and a collector. The light-weight periodic magnetic field coil provided by the invention is wound on a beam interaction region of the radial transit time oscillator, as shown in fig. 2, namely from the entrance of the beam interaction region to the tail end of the collector.
Setting the diode voltage U to 625kV and the diode current I12.2kA, an electron beam radius a of 1mm, a calculated correction coefficient k of 0.67, and a corrected Brillouin magnetic field B under relativistic conditionsb13700 Guss. From this, the periodic magnetic field peak value B can be calculated0If 19400Guss, the magnetic field parameter α is preferably 0.66, and the magnetic field period length z is 19.8 mm.
Referring to the specification and parameter table of a common enameled wire, in an actual situation, resin and the like for fixing a coil need to occupy a certain gap, and a copper core enameled wire with the diameter of 4mm is selected to design an exciting coil. The coil is wound from the radial direction of 30cm to the axial direction at two sides of the metal wall of the electronic channel, and the left side and the right side of the coil are respectively provided with 5 turns. After winding one layer, the second section is continuously wound at the interval of 6mm until the tail end of the collector, and the coil winding diagram is shown in figure 3, wherein the distance between every two excitation coils can be obtained by a dichotomy iterative calculation. The coils are connected in series, and the adjacent two coils in each section of excitation coil are supplied with currents with equal magnitude and opposite directions. The magnetic fields formed by the two adjacent left and right coils in the same section are same in direction above the position of the electron beam channel, and the magnetic fields formed by the two adjacent upper and lower coils are opposite in direction above the position of the electron beam channel, so that the superposed magnetic fields in the whole space are in cosine distribution, and the magnetic field distribution diagram is shown in fig. 4.
The propagation of the electron beam in the electron channel of the beam wave interaction region is shown in fig. 5, and it can be seen that the electron beam is well focused in the modulation chamber and the extraction chamber, and finally collected on the collector electrode, and the whole magnetic field plays the intended role. The power diagram of microwave output is shown in fig. 6, the device starts to start oscillating in 17ns, reaches saturation in 26ns, and outputs 1.89GW of power.
On the basis of electromagnetic simulation software, the aim of generating a superposed magnetic field with the same action effect is to obtain that 20 layers of the traditional uniform and dense winding excitation coil needs to be wound, but only 10 layers are needed in the invention, so that the quality of the whole coil can be greatly reduced, and the method has important significance in the aspect of light and small size of devices.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A light-weight periodic magnetic field coil applied to a high-power microwave source, wherein the high-power microwave source comprises a radial transit time oscillator, and the light-weight periodic magnetic field coil is characterized by comprising a plurality of sections of excitation coils which are uniformly arranged on the outer wall of a beam wave interaction region of the radial transit time oscillator at intervals, each excitation coil comprises a plurality of layers of densely wound solenoids which are oppositely arranged on two sides of the outer wall of the beam wave interaction region, a plurality of solenoids which are positioned on the same side of the beam wave interaction region are linearly arranged, and an insulator is arranged between two adjacent solenoids which are positioned on the same side of the outer wall of the beam wave interaction region;
the superposed magnetic field B (r) generated in the electron beam channel of the beam wave interaction area after the solenoids are electrified is distributed in a cosine way; wherein a peak value B of the superimposed magnetic field0Is the Brillouin magnetic field B of the electron beam under the corrected relativistic conditionbIs/are as follows
Figure FDA0003439449800000014
The magnetic field parameter alpha of the superposed magnetic field B (r) is 0-0.66 or 1.72-3.76.
2. The lightweight periodic magnetic field coil applied to a high power microwave source as claimed in claim 1, wherein the Brillouin magnetic field BbThe calculation formula of (2) is as follows:
Figure FDA0003439449800000011
brillouin magnetic field B of electron beam under the relativistic conditionbThe formula for calculating the correction coefficient k is:
Figure FDA0003439449800000012
in the formula I0Represents the current flowing into the diode in the radial transit time oscillator, and the unit is A; u represents the voltage across a diode in a radial transit time oscillator; a represents the radius of the electron beam generated by the diode in the radial transit time oscillator, in mm; epsilon0Represents the vacuum dielectric constant; eta0Represents the charge-to-mass ratio of electrons in kV; gamma represents a factor of relativity and gamma represents,
Figure FDA0003439449800000013
m0representing the resting mass, m the relativistic mass, c the speed of light, and e the elementary charge.
3. The lightweight periodic magnetic field coil applied to a high power microwave source as claimed in claim 1, wherein the magnetic field parameter α is calculated by the formula:
Figure FDA0003439449800000021
in the formula, L represents the length of a single solenoid.
4. The lightweight periodic magnetic field coil applied to high power microwave source of claim 1, wherein the period length z of the superimposed magnetic field B (r) is calculated according to the trajectory equation of the edge electrons of the electron beam under relativistic conditions:
Figure FDA0003439449800000022
wherein R represents the normalized beam radius of the electron beam,
Figure FDA0003439449800000023
r represents the electron beam radius; r is0Representing the cosine of the electron beamAn average radius; beta represents a space charge parameter of the electron beam,
Figure FDA0003439449800000024
5. the lightweight periodic magnetic field coil for high power microwave source as claimed in claim 1, wherein two adjacent solenoids on the same side are supplied with current with the same magnitude and direction, and two oppositely disposed solenoids are supplied with current with the same magnitude and opposite direction, so that the superimposed magnetic field b (r) generated by each solenoid in the electron beam channel of the beam interaction region is in cosine distribution.
6. The lightweight periodic magnetic field coil applied to a high power microwave source as claimed in claim 5, wherein the supply current I of each solenoid is set according to the configuration parameters of each solenoid, and the calculation formula of the supply current I is:
Figure FDA0003439449800000031
in the formula, a superposed magnetic field
Figure FDA0003439449800000032
j represents the current density in the case of continuous current distribution, j equals NI/[2L [0(R2-R1)]；R1、R2Correspondingly representing the inner and outer radius of each solenoid; 2L of0Represents half of the total length of the solenoid; n represents the total number of turns of the solenoid.
7. The lightweight periodic magnetic field coil for high power microwave sources of claim 6 wherein the configuration parameters of each of said solenoids are set accordingly according to the size of the beam interaction region of said radial time-of-flight oscillator.
8. The lightweight periodic magnetic field coil for high power microwave source of claim 7 wherein each of said solenoids is made by winding copper core enameled wire with a diameter of 4 mm.
9. The lightweight periodic magnetic field coil for high power microwave source as claimed in claim 1, wherein the insulator is made of insulating bakelite.
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