Kawata, S

Manabe, A

Mizuno, K

Watanabe, H

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Particle Accelerators, 1990, Vol. 32, pp. 229-234Reprints available directly from the publisherPhotocopying permitted by license only© 1990 Gordon and Breach, Science Publishers, Inc.Printed in the United States of AmericaELECTRON ACCELERATION BY AN ELECTROMAGNETIC WAVEWITH A STATIC MAGNETIC FIELD#SHIGEO KAWATA, ATSUSHI MANABE, HIROYUKI WATANABE ANDKATSUHIRO MIZUNODepartment of Electrical Engineering, Nagaoka#University of Technology, Nagaoka 940-21, JAPANDepartment of Applied Science, University ofCalifornia Davis, Davis, California 95616, U.S.A.Abstract A new mechanism is presented for high-energy electron acceleration by an electromagnetic(EM) wave with a static magnetic(B) field. Numericalanalyses and simulations show that this mechanismworks well for high-energy-electron acceleration.INTRODUCTIONA number of mechanisms have been proposed for high-energyparticle acceleration1 - 3 • In this paper we present a newmechanism for a high-energy electron acceleration by an EMwave. An EM wave traveling across a static magnetic fieldaccelerates high-energy electrons. The magnitude of thestatic magnetic field is surprisingly small compared withthe amplitude of the EM wave. The optimal magnitude ofthis static magnetic field is also discussed. Inaddition, a pulse EM wave whose profile is Gaussian, isalso disscussed for a realistic acceleration.ACCELERATION MECHANISMFigure 1 presents this mechanism for high-energy electronacceleration by an EM wave with a static magnetic field.A plane EM wave propagates at the speed of light in the +xdirection. The magnetic component of the wave is in the[1671]/229230/[1672] s. KAWATA ET AL.x-z plane and the electric one is in the x-y plane.yFIGURE 1 A mechanism of high-energy electronacceleration by a plane EM wave with aweak static magnetic field in free space.In the acceleration region indicated inthe figure, electrons can be acceleratedin -y direction by an electric component.If the system has no static magnetic field, anoscillating electron motion may be expected and theelectron cannot absorb the EM-wave energy. This comesfrom the symmetry of the EM wave in space. Our idea is toremove this symmetry by applying a static magnetic fieldBapp . The electron equation of motion and the energyequation are as follows:dPx/dt=-evy(Bz+Bapp)/c,dPy/dt=Fy=-e[(1-vx/c)Bz-vxBapp/c]d(mC 2Y)/dt=-eEy vy( 1 )(2 )(3 )Here Ey=Bz=Asin[k(x-ct)] and A is the amplitude of the EMwave. The speed of vy in Eq. (3) is determined by Eq.(2). The force in the y direction is proportional to thefactor of (1-vx/c)Bz-vx/cBapp. We can choose anestimation value of Bapp so that in the region of n<k(x-ct)<O this factor becomes quite small, that is,ELECTRON ACCELERATION BY AN EM WAVE [1673]1231and the electron trajectory is not influencedsignificantly, although Bz changes in the above sinfunction. In the remaining half-wave of 2 n (k(x-ct)(TI,that is, the acceleration phase, the force Fy enhanced tobe -e[(1-vx/c)IBzl+vxIBappl /c] and the electron isaccelerated in the -y direction. In addition, theelectron feels the force of -evy(Bz+Bapp)/c= +eIVy(Bz+Bapp)l/c in the +x direction, so the relativevelocity between the EM wave and the electron becomessmall in the acceleration phase. Thus the electron stayslonger in the acceleration phase. Consequently theelectron can be accelerated efficiently by the EM wave.NUMERICAL ANALYSESFirst, a single particle analysis is performed in thefixed fields in order to demonstrate this mechanism. Inthis case, the linearly polarized EM wave is infinitelycontinuous in the x direction. Figure 2 shows electronenergy versus the x coordinate. In this case, the initialelectron velocity is 0.95c in the x direction and theelectron has no vy initially. In this example, theamplitude of the EM wave is 0.1xEO' EO=1.02x107 /L volt/cm,L is the wavelength in cm, the space x coordinate isnormalized by L/20 and -Bapp /A=0.018 which is the optimalvalue of Bapp for this specified parameter set. Thenumerical integral of the relativistic equation of motionshows that the averaged Vx becomes about 0.98c in theacceleration phase in this case. By using this value ofVx and Eq. (4), we can estimate that Bapp is about -0.02A,which corresponds well to the optimal value employed inthis numerical integral.We also perform the 1 .5-dimensional(x,vx and vy )particle-in-cell(PIC) simulation1 ,2. The relativisticequation of motion and the Maxwell equations are solved inthe program self-consistently. In the simulation, themodel employed is nearly the same as that used in the232/[1674] S. KAWATA ET AL.above analysis, however there is a difference in thefinitude of the EM wave in the x space. At the start oft=O, the incoming EM wave exists infinitely only when x<O.The EM wave then propagates in the +x region and catchesup with electrons traveling with the velocity ofvx(t=0)=+0.95c. The wavelength 1 covers 20 space meshes.The x coordinate is normalized by 1/20. The total meshnumber is 1024. The initial number density of theelectron beam is nO=2.18x108 /12 cm-3 . The electrons aredistributed uniformly 0<x<20 and follow the Maxwelldistribution with the temperature of 1.0keV at t=O. Theoptimal Bapp is slightly different from the value employedin the above analysis because of the finitude of the EMwave, and -0.025xA in this case. As the boundarycondition, the perfect conductors are set at x=O and 1024.10 ,..-------------.,oo 200 400x600 aoo 1(XX)FIGURE 2 Electron energy versus x. After passingthrough one wavelength of an EM wave, theelectron absorbs the wave energy.Figure 3 represents the relativistic factor versusthe real space x. Figure 3 clearly shows the accelerationand scattering of electrons in our system. Some of theelectrons absorb energy up to 6.82xmc 2 . This maximumenergy is less than that obtained in the formeranalysis(see Fig.2). This difference comes from thefinitude of the EM wave.ELECTRON ACCELERATION BY AN EM WAVE [1675]1233co0'\l.f")>- 0'\'-0('V)~oq-516 526 536XFIGURE 3 Particle simulation results for ahigh-energy electron acceleration by an EMwave with a weak static field(Bapp )'shows the relativistic factor versus x.ELECTRON ACCELERATION BY GAUSSIAN PULSEIn order to apply this mechanism to a realisticacceleration of electron, 1 .5-dimensional numericalsingle-particle analyses are performed for the electronacceleration by the Gaussian pulse as shown in Fig. 4(a).The Gaussian pulse employed isFigure 4(b) presents the relativistic factor versus wavecoordinate. This result shows that our mechanism isapplicable for a realistic acceleration. In this exampleM=L/2, A=1 .64x106/L volt/em, L is the wavelength in em, xcoordinate is normalized by L/32. Figure 4(b) shows thatelectron can be accelerated well by a realistic Gaussianpulse.234/[1676] s. KAWATA ET AL.29.13(b)LJ"") (V)0 N0 00. N0.tdc:o+ N NNO >-~c:o a 000 I ~w~0"'\ 00 00 0I-48.56 -9.71 29.13 -48.56 -9.71X XFIGURE 4 (a) Gaussian pulse, (b) The relativisticfuctor versus x in the wave coordinate.Vx=0.9454C & Vy =0.2939C at time=O.CONCLUSIONSIn this paper, we proposed a new mechanism for high-energyelectron acceleration by an EM wave traveling across aweak static magnetic field, and demonstrated its viabilityand effectiveness by numerical analyses and particlesimulations.REFERENCES1. S. Kawata, A. Manabe, T. Yabe, S. Takeuchi, K. Sakaiand R. Sugihara, Jpn. J. Appl. Phys., 27, 163 (1988)and references therein.2. S. Kawata,A. Manabe and S. Takeuchi, Jpn. J. Appl.Phys., 28, 1704 (1989).3. W. Werner and H Hora, Laser and Particle Beams,1, 315 (1989).

Electron Acceleration By An Electromagnetic Wave With A static Magnetic field

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