EP0809271A2

EP0809271A2 - Electron gun

Info

Publication number: EP0809271A2
Application number: EP97303476A
Authority: EP
Inventors: Frederick Michael Mako; William Kalman Peter
Original assignee: Individual
Current assignee: Individual
Priority date: 1996-05-22
Filing date: 1997-05-21
Publication date: 1997-11-26
Also published as: CA2205989A1; CA2254137A1; IL120874A0; JPH1055763A; EP0809271A3; EP0900446A1; WO1997044804A1

Abstract

The present invention pertains to an electron gun. The electron gun comprises an RF cavity having a first side with an emitting surface and a second side with a transmitting and emitting section. The gun is also comprised of a mechanism for producing an oscillating force which encompasses the emitting surface and the section so electrons are directed between the emitting surface and the section to contact the emitting surface and generate additional electrons and to contact the section to generate additional electrons or escape the cavity through the section. The section preferably isolates the cavity from external forces outside and adjacent the cavity. The section preferably includes a transmitting and emitting screen. The screen can be of an annular shape, or of a circular shape, or of a rhombohedron shape. The mechanism preferably includes a mechanism for producing an oscillating electric field that provides the force and which has a radial component that prevents the electrons from straying out of the region between the screen and the emitting surface. Additionally, the gun includes a mechanism for producing a magnetic field to force the electrons between the screen and the emitting surface. The present invention pertains to a method for producing electrons. The method comprises the steps of moving at least a first electron in a first direction. Next there is the step of striking a first area with the first electron. Then there is the step of producing additional electrons at the first area due to the first electron. Next there is the step of moving electrons from the first area to a second area and transmitting electrons through the second area and creating more electrons due to electrons from the first area striking the second area. These newly created electrons from the second area then strike the first area, creating even more electrons in a recursive, repeating manner between the first and second areas.

Description

FIELD OF THE INVENTION

The present invention is related to electron guns. More specifically, the present invention is related to an electron gun that uses an RF cavity subjected to an oscillating electric field.

BACKGROUND OF THE INVENTION

The development of high-current, short-duration pulses of electrons has been a challenging problem for many years. High-current pulses are widely used in injector systems for electron accelerators, both for industrial linacs as well as high-energy accelerators for linear colliders. Short-duration pulses are also used for microwave generation, in klystrons and related devices, for injectors to perform research on advanced methods of particle acceleration, and for injectors used as free-electron-laser (FEL) drivers.
The difficulty in generating very high-current pulses of short duration can be illustrated by examination of a modern linac injector system. A good example is the system designed and built for the Boeing 120 MeV, 1300 MHz linac, which in turn is used as an FEL driver [J.L. Adamski et al., IEEE Trans. Nucl. Sci. NS-32, 3397 (1985) ; T.F. Godlove and P. Sprangle, Particle Accelerators 34, 169 (1990)]. The Boeing system uses: (a) a gridded, 100 kV electron gun; (b) two low-power prebunchers, the first operating at 108 MHz and the second at 433 MHz; and (c) a high-power, tapered-velocity buncher which accelerates the beam bunches up to 2 MeV. The design relies on extensive calculations with codes such as EGUN, SUPERFISH and PARMELA. A carefully tapered, axial magnetic field is applied which starts from zero at the cathode and rises to about 500 Gauss. With this relatively complex system Boeing obtains a peak current of up to about 400 A in pulses of 15 to 20 ps duration, with good emittance. The bunching process yields a peak current which is two orders of magnitude larger than the electron gun current. Space charge forces, which cause the beam to expand both radially and axially, are balanced by using a strong electric field in the high-power buncher, and finally are balanced by forces due to the axial magnetic field. The performance achieved by Boeing appears to be at or near the limit of this type of injector.
During the last few years considerable effort has also been applied to the development of laser-initiated photocathode injectors [M.E. Jones and W. Peter, IEEE Trans. Nucl. Sci. 32 (5), 1794 (1985); P. Schoessow, E. Chojnacki, W. Gai, C. Ho, R. Konecny, S. Mtingwa, J. Norem, M. Rosing, and J. Simpson, Proc. of the 2nd European Particle Accel.Conf. 606 (1990); K. Batchelor et al, Nucl. Instr. and Meth. in Phy. Res. A318, 372 (1992); S.C. Hartman et al, Part. Accel. Conf., IEEE Cat. 93CH3279-1, 561 (1993); I. Ben-Zvi, Part. Accel. Conf., IEEE Cat 93CH3279-1, 2962 (1993); I. S. Lehrman et al, Part. Accel. Conf., IEEE Cat. 93CH3279-1 3012 (1993); C. Travier, Nucl. Instr. and Meth. in Phy. Res. A340, 26 (1994)]. The best of these have somewhat higher brightness than the Boeing injector, but the reliability depends on the choice of photocathode material, with the more reliable materials requiring a larger laser illumination.

SUMMARY OF THE INVENTION

Micro-pulses are produced by resonantly amplifying a current of secondary electrons in an RF cavity operating in, for example, a TM₀₂₀ mode (Fig. 1) or a TM₀₁₀ mode (Fig. 2) [F. Mako and W. Peter, Part. Accel. Conf., IEEE Cat. 93CH3279-1 2702 (1993)]. Figure 1 shows a perspective view of the micropulse gun emitting electron-bunches in an annular geometry. Figure 2 shows a side view of the micropulse gun emitting electron-bunches in a solid bunch geometry. Bunching occurs rapidly and is followed by saturation of the current density in typically ten to fifteen RF periods. "Bunching" occurs by phase selection of resonant particles. The bunch that is formed is much shorter than the RF period which is due to the resonant nature of this process. Also, the micropulse gun produces a narrow bunch every RF period in the output direction. Bunch transmission is accomplished by use of a transparent grid. Localized secondary emission in the micropulse gun is dictated by material selection. Radial space charge expansion in the micropulse gun cavity can be reduced by using·either electric or magnetic focusing, or both. Radial electric focusing in the cavity is accomplished by a concave shaping of the cavity, as shown in Fig. 2. The grid not only allows transmission of bunches but can also provide an emitting surface for electron multiplication. A path for the RF current can be maintained by using a grid of wires. The double grid isolates an external accelerating field from "pulling out" non-resonant electrons which would form a dc baseline. Also, the two grids are electrically isolated to allow for dc biasing to create a barrier for low energy electrons. Axial and radial expansion of the bunch is minimized outside the micropulse gun cavity by using various combinations of rapid acceleration, electric and magnetic focusing.
This micro-pulse electron gun should provide a high peak power, multi-kiloampere, picosecond-long electron source which is suitable for many applications. Of particular interest are: high energy picosecond electron injectors for linear colliders, free electron lasers and high harmonic RF generators for linear colliders, or super-power nanosecond radar.
The present invention pertains to an electron gun. The electron gun comprises an RF cavity having a first side with an emitting surface and a second side with a transmitting and emitting section. The gun is also comprised of a mechanism for producing an oscillating force which encompasses the emitting surface and the section so electrons are directed between the emitting surface and the section to contact the emitting surface and generate additional electrons and to contact the section to generate additional electrons or escape the cavity through the section.
The section preferably isolates the cavity from external forces outside and adjacent the cavity. The section preferably includes a transmitting and emitting screen. The screen can be of an annular shape, or of a circular shape, or of a rhombohedron shape.
The mechanism preferably includes a mechanism for producing an oscillating electric field that provides the force and which has a radial component that prevents the electrons from straying out of the region between the screen and the emitting surface. Additionally, the gun includes a mechanism for producing a magnetic field to force the electrons between the screen and the emitting surface.
The present invention pertains to a method for producing electrons. The method comprises the steps of moving at least a first electron in a first direction. Next there is the step of striking a first area with the first electron. Then there is the step of producing additional electrons at the first area due to the first electron. Next there is the step of moving electrons from the first area to a second area and transmitting electrons through the second area and creating more electrons due to electrons from the first area striking the second area. These newly created electrons from the second area then strike the first area, creating even more electrons in a recursive, repeating manner between the first and second areas.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, the preferred embodiment of the invention and preferred methods of practicing the invention are illustrated in which:
Figure 1 is a perspective view of the micropulse gun for a hollow beam using the TM₀₂₀ mode. The inner conductor is not shown.
Figure 2 is a schematic of micropulse gun for solid beam using the TM₀₁₀ mode. This side view of solid beam micro-pulse gun cavity showing double grid and emitting and transmitting surfaces. Beam pulses and concave shaping of the micropulse gun cavity are shown. Figure is not to scale. A coaxial feed or side coupling or coupling loops can be used for RF input (not shown).
Figure 3 Plot of current density vs. time for simulation with RF frequency 2.85 GHz and α_o = eV _o/(mω² d ²) = 0.373. d = 1.5 cm with peak RF voltage amplitude 153 kV.
Figure 4 Comparison of saturated current density in kA/cm² versus frequency for simulation and analytic theory for a gap length of d = 1.0 cm and drive parameter α_o = eV _o/(mω² d ²) = 0.373.
Figure 5 Saturated Current Density vs Drive Voltage, f = 2.85 GHz. The curves are for different gap spacings.
Figure 6 Micro-Pulse Width vs Drive Voltage, f = 2.85 GHz.
Figure 7 Emittance growth due to double-grid extraction with an injection beam energy of 114 kV. The wire thickness is set 0.1 mm.
Figure 8 Experimental Data: Current trace of the micropulse gun Micro Bunches.
Figure 9 Expansion of micro-pulse from space charge during acceleration, neglecting energy spread. The acceleration field is 50 MV/m and the axial space charge electric field is 1.33 MV/m (or about 35 nC/cm³).

DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to the drawings wherein like reference numerals refer to similar or identical parts throughout the several views, and more specifically to Figure 2 thereof, there is shown an electron gun 10. The electron gun 10 comprises an RF cavity 12 having a first side 14 with an emitting surface 16 and a second side 18 with a transmitting and emitting section 20. The gun 10 is also comprised of a mechanism 22 for producing an oscillating force which encompasses the emitting surface 16 and the section 20 so electrons 11 are directed between the emitting surface 16 and the section 20 to contact the emitting surface 16 and generate additional electrons 11 and to contact the section 20 to generate additional electrons 11 or escape the cavity 12 through the section 20.
The section 20 preferably isolates the cavity 12 from external forces outside and adjacent the cavity 12. The section 20 preferably includes a transmitting and emitting screen 24. The screen 24 can be of an annular shape, or of a circular shape, or of a rhombohedron shape.
The mechanism 22 preferably includes a mechanism 26 for producing an oscillating electric field that provides the force and which has a radial component that prevents the electrons 11 from straying out of the region between the screen 24 and the emitting surface 16. Additionally, the gun 10 includes a mechanism 28 for producing a magnetic field to force the electrons 11 between the screen 24 and the emitting surface 16.
The present invention pertains to a method for producing electrons 11. The method comprises the steps of moving at least a first electron 11 in a first direction. Next there is the step of striking a first area with the first electron 11. Then there is the step of producing additional electrons 11 at the first area due to the first electron 11. Next there is the step of moving electrons from the first area to a second area and transmitting electrons through the second area and creating more electrons 11 due to electrons from the first area striking the second area. This process is repeated until the device is shut off by removing the RF power source.
A schematic of one embodiment of the proposed device is given in Figures 1 and 2. Although the design shown is not necessarily optimum it provides a basis for describing the invention. Shown in figures 1 and 2 is a side view of a cylindrically symmetric device. RF power may be fed into the cavity through several means including: a low impedance coaxial transmission line connected to the back perimeter of the cavity, side coupling using a tapered waveguide or coupling loops. The appropriate mode is then set up in this case a TM₀₁₀ for a circular cavity (as in Fig. 2) or a TM₀₂₀ for the circular cavity as in Figure 1. An annular bunch is generated by secondary emission at the second peak of the electric field in the cavity operating in a TM₀₂₀ mode (Fig. 1). The first peak may be eliminated by placing an inner conducting cylinder at the first zero of the TM₀₂₀ mode. In Figure 2 a solid bunch is created on the axis by secondary emission. The right wall of the cavity in Figure 2(also see detail) is constructed with a transmitting double screen or grid which allows for the transmission of electron bunches. The crossed wires of the grid maintain a path for the RF current. The double grid isolates an external electric field from pulling out non-resonant electrons. Also, the grids are electrically insulated to allow for biasing to create a barrier for unwanted electrons.
To conceptualize how rapidly the current density can build up in the micropulse gun cavity a simplified model is presented which excludes space charge, transit time, amplitude and phasing effects but shows the principle behind utilizing multi-pacting for the micropulse gun. In Fig. 2 is shown an RF cavity operating in for example a TM₀₁₀ mode. Assume that at the grid-ded wall of the cavity there is a single electron at rest on axis, which transits the cavity in about one-half the RF period and is in proper phase with the field. This electron is accelerated across the cavity and strikes the surface S. A number δ₁ of secondary electrons are emitted off this electrode, where δ₁ is the secondary electron yield of surface S. Assume the electrons transit the cavity in one-half the RF period and they are in proper phase with the field, these electrons will be accelerated back to the grid. After reaching the grid, δ₁ T electrons will be transmitted, where T is the ratio of transmitted to incident electrons for the grid. The number of electrons which are absorbed by the grid is then δ₁(1-T). After one cycle the number of electrons that are produced by the grid is δ₂[δ₁(1-T)], where δ₂ is the grid secondary yield. To have electron gain, the number of secondaries must be greater then one, i.e. δ₂δ₁(1-T) > 1. Current amplification occurs by repeating this process. This is analogous to a laser cavity with the grid acting as a partially-silvered mirror. The gain of electrons after N RF periods is G = [δ₂δ₁(1-T)]^N. If there is a "seed" current density J _seed in the cavity initially, then after N RF periods the current density will be given by J = GJ _seed= J _seed[δ₂δ₁(1-T)]^N , until space-charge limits the current density. For a very low seed current density a high current density can be achieved in a very short time. For example, if δ₂ = δ₁= 8, T = 0.50, and J _seed= 1.3 x 10^-12 A/cm², in ten RF periods J =1500 A/cm²!
The seed current density J _seed can be created by several sources including: thermionic emission, radioactivity, field emission, cosmic rays, a spark or ultraviolet radiation.
The secondary emission yield δ is defined to be the average number of secondary electrons emitted for each incident primary electron and is a function of the primary electron energy ε. δ for all materials increases at low electron energies, reaches a maximum δ_max at energy ε_max, and monotonically decreases at high energies. Table I gives some commonly used materials with high and low values of δ [D.E.Gray(coord. Ed.), Amer. Inst. of Physics Handbook, 3rd Edition, McGraw-Hill; E. L. Garwin, F. K. King, R. E. Kirby and O. Aita, J. Appl. Phys. 61, 1145 (1987); A. R. Nyaiesh, et al., J. Vac. Sci. Tech. A, 4, 2356 (1986); G. T. Mearini, etal., Appl. Phys. Lett. 66 (2), 242 (1995)]. Table I

Secondary emission coefficient of some common materials.

Material δ _max ε _max (keV)

GaP+Cs (crystal) 147 5

Diamond +Cs 55 5

MgO (crystal) 20-25 1.5

TiN coating 1-1.6 0.3
A universal yield curve good for all materials (and experimentally verified) for normal primary incidence is given by δ = δ_max (2ε/ε_max)/[1+(ε/ε_max)^1.85(2Z/A)] where Z and A are the arithmetic mean atomic number and atomic weight, respectively [B.K. Agarwal, Proc. Roy. Soc. 71, 851 (1958)]. At 2.85 GHz and for a 1.5 cm cavity gap the particle energy turns out to be about 114 keV. The yield for diamond at 114 keV is ≈ 7.7. If T = 0.5, there would be gain since δ₂δ₁(1-T) > 1, (assuming δ₂ = δ₁ ).
Several photomultipliers (RCA C31024, RCA C31050 and RCA 8850) are built with GaP dynodes. GaP is not sensitive to oxygen but is sensitive to water. With very thin coatings on the surface of GaP, it can be made to allow secondaries to leave and at the same time prevent contamination. Also, GaP can be doped to eliminate charge build-up. Thus GaP could be an excellent candidate at high energy (up to 100's of keV). MgO is a good candidate for lower particle energy (<60 keV) and would have to be applied in a thin layer in order to minimize charge build-up. Another very robust emitter material that is currently under intensive study is diamond film [M.W. Geiss, et al., IEEE Electron Device, Letters, 12, 8 (1991)]. Single crystal alumina (sapphire) or polycrystalline alumina are also excellent robust emitters.
The entire MPG cavity (except for the specified secondary emission sites) needs to be built with a low secondary emission coefficient. Cavity surface coatings can reduce secondary emission and also isolate electrical whiskers from the cavity and serve as a trap for slow electrons [W. Peter, Journal of Applied Physics 56, 1546 (1984)]. CaF₂ and TiN [E. L. Garwin, F. K. King, R. E. Kirby and O. Aita, J. Appl. Phys. 61, 1145 (1987); A. R. Nyaiesh, et al., J. Vac. Sci. Tech. A, 4, 2356 (1986)] are excellent candidates for cavity coatings. Also, cavities built from 304 stainless steel or titanium work well for the low secondary emission areas.
Secondary emission involves electron diffusion, which implies finite emission time. A simple diffusion analysis shows that the emission time for several emitters is several picoseconds or longer [P.T. Farnsworth, J. Franklin Institute, 218, 411 (1934)]. This emission time will limit the maximum cavity frequency.
Secondary electrons are not emitted normal to the surface, but follow an angular distribution which is nearly independent of the angle of incidence of the primary electrons. This angular distribution comes from secondary electron scattering in the material which ends up as emittance in the beam. Secondary electrons follow an angular distribution according to a cos²θ law [J.L. H. Jonker, Philips Research Repts. 12, 249 (1957)].
An estimate of the normalized transverse emittance can be obtained from the expression, ε_n=2r _b(kT _t/mc ²)^1/2 where, kT _t represents the average transverse thermal kinetic energy, r _b the beam radius and mc ² the electron rest mass energy. The secondary electron energy distribution typically has a spread of much less then an eV. We will take r _b = 1 mm, and since most of the particles have been shown to come out at ∼30° then kT _t is about 0.25 eV. From the above equation the normalized emittance is 1.4 mm-mrad. This emittance is comparable to that achieved from thermionic emitters or photo-cathodes. Since the angular distribution or emittance of the secondary electrons does not depend on the angle of incidence of the primary electrons, the emittance does not increase on successive RF periods inside the cavity.
The preceding discussion has focused on the secondary emission yield at a constant temperature, essentially room temperature. In high power RF cavities the electrodes become hot. However, temperature has little effect on the secondary emitters for the micropulse gun [G. Blankenfeld, Ann. Physik 9, 48 (1950); J.B. Johnson and K.G. McKay, Phys. Rev. 91, 582 (1953); A.J. Dekker, Phys. Rev. 94, 1179 (1954); A.R Shuylman and B.P. Dementyev, Sov. J.Tech. Phys. 25, 2256 (1955)].
In this section we will describe the solution to the self-consistent steady state or saturation current density for a beam that is already presumed to be "bunched". Reference [F. Mako and W. Peter, Part. Accel. Conf., IEEE Cat. 93CH3279-1 2702 (1993)] gives a detailed evaluation of the saturated current density. The axial bunch length (z-axis) is s_o, the axial gap spacing between two parallel metal grounded plates or cavity walls is d, and the bunch density is n. We evaluate the equations of motion for electrons "attached" to the front ("f") and back ("b") of the bunch. The quantities E _o and E _sc are the magnitudes of the RF and space charge electric fields, respectively. Resonance is imposed on the particles, i.e., the particles are forced to cross the gap d in half an RF period. We now define some quantities, α _o = eE _o /mω² d, α _s = eE _sc /mω² d, E _sc = nes _o/2ε _o where e,m are the electron charge and mass respectively, ω is the radian frequency and ε_o is the permittivity of free space, for use in the analysis that follows.
The saturated bunch current density inside the cavity can be determined from the above evaluation and validated with simulation , and in practical units is expressed as, $J {(A/cm}^{2}) = 145.5 f^{3} (GHz) d^{1.75} {(cm)[α}_{o} - 0.2126]$
for 0.2126 ≤α_o≤ 0.38. It can be seen in Eq. (1) that the current density scales with frequency like ω³. This result is also derivable from the time-dependent current-voltage relation in a diode [A. Kadish, W. Peter, and M.E. Jones, Appl. Phys. Letters 47, 115 (1985)]. The ω³ scaling law is an important characterization of the micropulse gun. In going from 1 to 12 GHz the current density increases from Amp's/cm² to tens of kA/cm² (with variable α₀ and d). α₀= 0.373 gives the maximum saturated current density and at values greater than this there is no resonance. The ω³ scaling law results from above will be compared to simulation results where we find excellent agreement between theory and simulation. The corresponding electric field to maintain resonance requires only modest gradients.
It is important to estimate the likelihood of electrical breakdown in the micropulse gun. Kilpatrick's criterion [W.D. Kilpatrick, Rev. Sci. Inst. 28, 824 (1957)] is based phenomenologically on electrical breakdown due to secondary electron emission from ion bombardment. However, with advances in cleaning, conditioning and better vacuum techniques (that do not introduce contaminants), Kilpatrick's criterion overestimates the likelihood of breakdown by a factor of two or three for cw [R.A. Jameson, High-Brightness Accelerators, Plenum Press, 497 (1988)] and five to six for short pulses [S.O. Schriber, Proc 1986 Linear Accelerator Conference, June 2-6 (1986)] . A more recently established breakdown result comes from J. W. Wang at SLAC [J. W. Wang, SLAC-Report-339 July (1989)]. Wang expressed this formula in the form, E _o(MV/m) = 195 [f (GHz)]^1/2 where E _o is the peak surface electric field. For a cavity operating at 2.85 GHz, the critical surface electric field is 329 MV/m. The required resonant electric field in the micropulse gun is substantially lower than the critical surface field. With gap lengths between 0.5 and 2 cm and α_o = 0.373 the resonant field varies from 3.4 to 13.6 MV/m. Thus, breakdown is not a problem in the micropulse gun cavity.
The sections below show high current density, short pulse operation is possible with the micropulse gun.
The micropulse gun has been fully characterized using an FMT developed proprietary 2 1/2-D relativistic electromagnetic PIC code FMTSEC (that includes secondary emission). Input parameters for the micropulse gun are: RF voltage, frequency, cavity gap spacing, and magnetic focusing field. Output parameters are: current density, particle energy, transverse emittance and pulse width. Figure 3 shows the current density as a function of time for: f = 2.85 GHz, d = 1.5 cm, and V _o= 153 kV. Current density is evaluated near the exit grid (right side, Fig. 2). A positive current density is the current that travels from right to left. A negative current density describes the exiting beam. Current asymmetry occurs because the positive/negative beam pulses have substantially different charge densities and velocities at the exit grid. In Fig. 3 at a gap length of 1.5 cm, the saturated current density J _s after about 10 RF periods is 1150 A/cm² at V _o= 153 kV with α₀ = 0.373.
To strengthen the understanding of the micropulse gun, theory and simulation are compared in this section. The saturated current density is defined to be the peak current density after 10 to 15 RF cycles, i.e. where the amplitude becomes constant. A number of computer runs at various frequencies were performed to determine the current density inside (with T = 0) the micropulse gun. Fig. 4 shows the results from several simulations for the saturated current density J _s vs. RF frequency for a cavity with a 1.0 cm gap length and for α₀ = 0.373. The curve obeys a power law J _s ∝ ω ³ . For f =2.85 GHz the saturated current density is about 500 A/cm². Excellent agreement is shown between theory and simulation for the ω³ scaling law. Note that V _o ∝ ω² must be maintained for resonance at fixed α_o.
The saturated current density rises approximately linearly with the drive voltage, α_o (= eV ₀/mω² d ²), within the resonance window (Fig. 5). Each curve is a spline fit to the FMTSEC simulation data. The saturated current density is the peak current density, after 10 to 15 cycles, from the current density vs time traces. The current density plots also show the "tuning range" for the micropulse gun. A very tolerant tuning range is a key result. Even if the electric field changed by 30% from, say, beam loading, resonance would still occur but at a lower current density.
Figure 6 shows that the micro-pulse width can be adjusted using the drive voltage. Depending on gap spacing and α₀ the pulse width can be adjusted from 1.5% to 10% of the rf period. For the case: α₀ ≈ 0.373, the bunch length is 7 ps at a frequency of 2.85 GHz.
The bunch energy per rf period that is transmitted out of the cavity is given by, E _bt = ε _p N _p T where ε_P is the particle energy at the peak of the energy distribution, N _P is the number of particles in a bunch inside the micropulse gun cavity. There is one bunch transmitted per RF period from the micropulse gun. The RF power provides all the energy for the left- and right-traveling bunches inside the cavity. Therefore, the RF energy that feeds one bunch in an RF period is given by, E _rf = 2ε_p N _p.
Next the particle energy ε_p will be determined. Consider a particle at the center of a bunch. This particle is also at the peak of the distribution. A sinusoidal electric field is applied to this particle at a phase angle of ϕ. For the particle to be resonant, it must cross the gap spacing in ϕ+π. PIC simulation shows that the initial phase angle ϕ is near zero. The resulting particle energy can be shown to be, ε_p=2eV _oα_o where e is the electron charge. The transmitted power in a bunch, P _bt, and the RF power required to drive a bunch, P _rf,in , is then $P_{bt} = 2 {eV}_{o} α_{o} N_{p} Tf$
$P_{rf,in} = 4 {eV}_{o} α_{o} N_{p} f .$
For example, if f = 2.85 GHz, d = 1.5 cm, V _o= 153 kV, α_o= 0.373 and T = 0.5, then N _P = 2 x 10⁹, P _rf,in= 208.2 kW and P _bt = 52 kW. The stored energy in the cavity is given by U = ε _o[π(R _m)² d] [v ₀ /d]² [J ₁ ²(x _cm )/2] where, x _om are the zeros of the J ₀ Bessel function and R _m is the resonant cavity radius. For f=2.85 GHz, m=1, d=1.5 cm, R ₁ =4.03 cm, V _o= 153 kV and for α₀=0.373. The stored energy is U=9.49 mJ. Next the loaded Q _L of the cavity can be estimated from Q _L = ωU/P _rf,in . For the example at 2.85 GHz the Q _L loaded by the beam is 816. To minimize power losses to the wall, it is desirable to have an unloaded Q _U >> Q _L. A coated copper cavity could be used to keep the cavity secondary emission low and the unloaded Q _U high. The fill time for the cavity is given by τ_f = 2Q _L/ω. Again for the 2.85 GHz case the fill time is, roughly 260 RF periods. Since the fill time is long compared to the current density saturation time, the transmitted beam current rise time is determined by the fill time which in this case is 91 ns.
FMT has performed 3-D PIC code (SOS) simulations to determine bunch emittance growth from the micropulse gun grid. Emittance was evaluated before and after the grids. Emittance can be substantially reduced by using a dense grid of wires, but at the expense of reducing transmission. Results have shown a lower emittance than anticipated. This occurs because the transverse electric field at the grid wires is small during bunch extraction. The inherent mechanism for bunch formation captures the bunch at a phase angle near zero. Bunch arrival at the grid π/ω later occurs when the electric field is again near zero. This is a big advantage for the micropulse gun as compared to a Pierce gun with a grid which exposes electrons to the maximum field. Input parameters are supplied from the results of FMTSEC. They are: εp = 114 keV, J _s = 1150 A/cm², τ = 7 ps, bunch area 4 mm², 2 x 10⁹ electrons in a bunch, initial normalized emittance before the grid = 1.6 mm-mrad (the contribution from the secondary emission process is 1.4 mm-mrad and the micropulse gun 0.84 mm-mrad) for a frequency of 2.85 GHz and gap d = 1.5 cm.
Figure 7 shows the beam emittance and transmission versus the grid wire density for a wire thickness of 0.1 mm and density of 28 wires/cm the results give a transmission of -53% and a total (all sources) normalized transverse beam emittance of about 2.3 mm-mrad. This final emittance is nearly the same as the emittance before the double grid.
The grids will heat up primarily due to electron beam impact. Consider a molybdenum grid with a thin coating of secondary emitting material. A thin layer of secondary emitter is used in order to reduce charge build-up, thus most of the charge is deposited in the molybdenum. Preferably the material will be made electrically conducting by doping, thus eliminating charge build-up.
The average power/unit area delivered to the molybdenum grid structure is $P_{avg} {= 2α}_{0} (1 - T) V_{0} J_{S} f τ f_{r} τ_{d}$
where, τ_d and f _r are the macro-pulse duration and repetition rate, respectively, and τ is the FWHM of the micro-pulse current and f is the cavity drive frequency. If T = 0.50, f = 2.85 GHz, d = 1.5 cm, V ₀ = 153 kV, J _s = 1150 A/cm², α₀ ≈ 0.373, τ=7 ps, f _r = 0.2 kHz and τ_d = 1.0 µs then P _avg = 262 W/cm².
To estimate the temperature rise, we assume that the power (P _avg) flows only conductively through the molybdenum grid wires from the center to edge of the circular grid area (Fig. 2). If the grid material has a thermal conductivity of k and axial thickness Δt (i.e, thickness in the direction of beam motion), then the temperature difference (ΔT _g) between the center and edge (radius = l) radius is given by: ΔT _g = P _avg l ² /(2kΔt). For a molybdenum grid, k = 1.39 W/cm-°C, Δt = 0.038 cm, l = 0.1 cm, we get ΔT _g = 24.8 °C. The grid will not get hot and this temperature rise is not destructive to the secondary emitter.
A proof-of-principle micropulse gun experiment has been conducted. [J. Shiloh, F. Mako and W. Peter, Proceedings of the 11th Int. Conf. on High Power Particle Beams, Karel Jungwirth, Jiri Ullschmied, Eds. Institute of Plasma Physics, Czech Academy of Sciences, Prague, 437 (1996).] The micropulse gun cavity is designed for a TM₀₁₀ mode and is fed from an L-band (1.2-1.3 GHz) magnetron which delivers about 50 kW to the beam load. We developed a direct charge measurement system for the bunches using a 50 GHz bandwidth sampling scope (HP-54720A). The magnetron is operated at 300 Hz repetition rate. Each microwave pulse lasts for 5 µs and contains about 6500 electron bunches (1 for each RF period). A very accurate timing system is used to trigger the scope so that, if the micropulse gun pulses are reproducible, it is possible to measure the current as a function of time. The collected charge generates a signal that propagates through a custom made 50 ohm, 50 GHz coaxial feedthrough. We were successful in performing a direct measurement of the bunches and were able to prove the feasibility of the micropulse gun concept.
When we use the fast 50 GHz sampling oscilloscope and look at a 5 ns slice of the macropulse we can see the micropulses.
Figure 8 shows a measurement of the bunches on a 500 ps/div time scale. The bunches appear with the periodicity of the RF field (-800 ps), in excellent agreement with simulation. More detailed measurements show that the actual bunch length is about 50 ps (FWHM) which is about 6.5 % of the RF period at a current density of about 22 A/cm². This is about 1.1 nC or 7 x 10⁹ electrons per RF period.
In this section the axial spatial expansion and temporal bunching are examined by including either the axial space charge electric field or an initial energy spread combined with rapid acceleration. Phase focusing is not included. The expansion is examined starting from just outside the micropulse gun cavity and through the high energy acceleration region. We will derive an approximate expression for the space charge expansion first. The axial Lorentz equation can be written in the following form $\frac{∂β}{∂ t} = \frac{α_{a}}{γ^{3}} + \frac{α_{sc}}{γ}$
where α_a = eE _a /mc and α_sc = eE _sc/mc. E _a and E _sc are the accelerating and space charge electric fields, respectively. Note that E _sc is the space charge field in the moving frame of the micro-pulse. The inductive electric field reduction of the space charge electric field is taken into account in Eq. (5) by the additional γ². The equation for the time evolution of the length, s, of the micro-pulse is given by $\frac{∂_{S}}{∂_{t}} {= (β}_{c} {-β}_{f}) c$
where the subscript c refers to the center of the micro-pulse and the subscript f refers to the front face of the micro-pulse. Define the change in γ from the front to the center of the micro-pulse by δγ= γ_f-γ_c. Assume that δγ/γ_c << 1, γ_c >> 1, γ_f>> 1. From Eqs (5), (6), the definition of δγ, dropping the subscripts on γ and assuming that γ = γ_o + α_a t where γ_o is the initial value of γ we obtain the following pair of equations
$\frac{δγ}{γ} = \frac{E_{sc}}{{γγ}_{o} E_{a}}$
where Δs, s_o are the change and initial length of the micro-pulse. Consider the micropulse gun operating at 2.85 GHz, d= 1.5 cm, V _o = 153 kV, a bunch radius = 1.13 mm and T = 0.5. Then the pulse duration is τ = 7 ps, the particle energy is 114 keV, and the transmitted number of electrons is 1 x 10⁹. These results are equivalent to s _o = 0.115 cm, γ_o = 1.2, and E _sc = 1.33 MV/m. Also consider the following parameters γ = 11 and E _a= 50 MV/m. The resulting length change is 2.3% and the energy spread due to space charge 0.2%. Equations (7,8) don't estimate spread correctly since γ_o is not large. Figure 9 shows numerical integration for the spatial bunch length and temporal pulse width versus energy. The bunch length expands by 10.7%. The pulse is compressed to 4.3 ps. Additional bunching can be accomplished if phase focusing is considered.
The expansion of the micro-pulse due only to an initial energy spread can be calculated by a similar method as outlined above for space charge expansion. We present the result:
For the above sample parameters and an initial Δγ/γ_o= 2% then a 7.4% expansion occurs along with a temporal pulse reduction to 4.1 ps. Numerical integration gives a 3.9% expansion of the spatial bunch length and a temporal compression to 4 ps.
Although the invention has been described in detail in the foregoing embodiments for the purpose of illustration, it is to be understood that such detail is solely for that purpose and that variations can be made therein by those skilled in the art without departing from the spirit and scope of the invention except as it may be described by the following claims.

Claims

An electron gun comprising:
an RF cavity having a first side with an emitting surface and a second side with a transmitting and emitting section; and

a mechanism for producing an oscillating force which encompasses the emitting surface and the section so electrons are directed between the emitting surface and the section to contact the emitting surface and generate additional electrons and to contact the section to generate additional electrons or escape the cavity through the section.
A gun as described in Claim 1 wherein said section isolating the cavity from external forces on outside the cavity and adjacent.
A gun as described in Claim 2 wherein the section includes a transmitting and emitting double screen.
A gun as described in Claim 3 wherein the mechanism includes a mechanism for producing an oscillating electric field that provides the force and which has a radial component that confines the electrons to the region between the screen and the emitting surface.
A gun as described in Claim 4 wherein the screen is of an annular shape.
A gun as described in Claim 4 wherein the screen is of a circular shape.
A gun as described in Claim 4 wherein the screen is of a rhombohedron shape.
A gun as described in Claim 4 including a mechanism for producing a magnetic field to force the electrons to stay between the screen and the emitting surface.
A method for producing electrons comprising the steps of:
moving at least a first electron in a first direction;

striking a first area with the first electron;

producing additional electrons at the first area due to the first electron;

moving electrons from the first area to a second area; and

transmitting electrons through the second area and creating more electrons due to electrons from the first area striking the second area.