Ishizuka, H

Toyama, H

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Particle Accelerators1973, Vol. 5, pp. 237-240© Gordon and Breach, Science Publishers Ltd.Printed in Glasgow, ScotlandELECTRON ORBITS IN THE ERA (ELECTRON RING ACCELERATOR)WITH AN ELECTROSTATIC-TYPE INFLECTOR SYSTEMH. TOYAMAtInstitute of Plasma Physics, Nagoya University, Nagoya, JapanandH.ISHIZUKAFaculty of Science, Tokyo University of Education, Tokyo, JapanElectron orbits in the ERA with an inflector system are calculated. The operational condition for effective captureof the electron beam is presented.1. INTRODUCTIONThe ERA (Electron Ring Accelerator) in theInstitute of Plasma Physics is now under construc-tion. The assembly of the ERA system has ascomponents a field emission high intensity electrongun, a post accelerator and a compression system ina large vacuum chamber. The beams are injectedinto the chamber through the snout and arecaptured with the assistance of the inflectors. Theinflector system is an electrostatic one, which canproduce easily a rectangular pulse with very shortrise and fall times. The electrodes are set along twoconcentric circles in the vacuum chamber as shownin Figure 1. They consist of copper plates dividedazimuthally into four equal sections. A snout ismade of ferromagnetic material with current-carrying conductors to shield the static magneticfield and the pulsed electric field.! It extends close tothe outer electrode and the electron beam is injectedtangentially into the region between the plates. Innormal operation, a pulsed radial electric field isapplied uniformly along the total circumference.In this paper we have calculated electron orbits toget operational conditions for effective capture ofelectrons.oInflectorElectrodeFerromagnetic Materialwith a ct)rrent- carryingConductor2. CALCULATIONThe equation of motion of a particle of charge e andmass m in a combined electric and magnetic field isSection A-AFIGURE 1. Schematic diagram of the inflector system.t Present address: Faculty of Science, University of Tokyo,Tokyo, Japan.d-(my) = e(E+vxB).dt(1) In cylindrical coordinates Eq. (1) becomesd ·2 •dt (mf) = mr(} +eEr +e(rlJBz - iBo), (2)238 H. TOYAMA AND H. ISHIZUKAO~t~'rotherwisewhere the dots indicate differentiation with respectto time. For relativistic motion m = moy, where mois the rest mass of the particle and(5)Introducing nondimensional variablesx = tiT,Y1 = rlR,andeBoB=--T,mowhere c is the velocity of light in free space, and T,R, Eo, and Bo are scaling factors.In the inflector system of the ERA, electric andmagnetic fields are as follows:Eo = Ez = Br = Bo = 0,{EoEr = 0[ R BBz(r )JBz = Bo 1+ - - - - 1Bo Br RY2 = (),Y3 = zlR,Y4 = (TIR)yf,Ys = (TIR2)yr2e,Y6 = (TIR)yi,we can write Eq. (2) in the formdYedx t =!i(X'Y1'Y2'··· 'Y6)' i = 1,2,··· ,6,11 = Y4/y,12 = YS/(YY1 2),13 = Y61y,14 = Y/3 +Aer+B(~bz- Y6 bO)'YYl YYl Y15= Y{Ae6+B(~6br- ~4 bz)l16 = Aez+B(Y4 bo- ~br),y YYl[ (R)2( Y 2 )J1/2Y= l+cT Yl+y:2+Y/ ,ea. = Ea.IEo,btl = Ba.IBo (Ct = r, (), z),A = eEoR (CT)2m oc2 R(6)(7)(8)(9)(10)(11)(12)whereNumerical calculations of the electron trajectory inthese fields were performed on a HITAC-8500digital computer by using Eqs. (6-13) with thefollowing initial conditions and parameters:Initial conditions:r = 27 cm, () = 0, z = 0, Vr = 0, Vz = 0,electron energy = 600 keY.Parameters:radius of equilibrium orbit '0 = 22 em,Eo = -0.2, -0..4, -0.6, -0.8, -1.0, -1.2kV/cm,'r = 1,3, 5, 7, 9 nsec,n = 0.7.The gyration period on the equilibrium orbit is 5.2nsec. Typical examples of the orbits are shown inFigures 2,3,4 using FACOM GRAFIC DISPLAYSystem. 2 A dotted circle E is the equilibrium orbit.When the electric field Eo is zero (correspondingto Figure 2), the electron does not clear the snout atthe 2nd revolution (Jl- n = 0.55). In the case ofEo = -0.4 kV/cm and 'r = 7 nsec, the electronclears the snout as shown in Figure 3, but theamplitude of the betatron oscillation is rather larg1e.ERA INJECTION ORBITSFIGURE 2. Electron orbit. Eo= O. S: Start. A-dotted circle E: Equilibrium orbit.FIGURE 3. Electron orbit. Eo = -0.4 kVjcm and 't" = 7 nsec.239240 H. TOYAMA AND H. ISHIZUKAFIGURE 4. Electron orbit. Eo = -0.8 kVjcm and r = 9nsec.It is desirable that the electron is moving nearly onan equilibrium orbit r = r 0 at the instant theelectric field is' turned off. In the system underconsideration, the right side of Eq. (2) becomes asfollows:v2mol' - +eEo+evBrmoyv2 1 (x)= --1 (/ ) +eEo+evBo I-n-ro + x ro ro= e[Eo+VBoX(_I- -~)J,ro+x rowhere v = rO and x = r - ro. Thus, the electric fieldrequired to balance the force isEo = -1.03 kV/cm,in the case of the electron energy = 600 keY,r 0 = 22 cm, and x = 5 cm. When an electric fieldclose to but less than lk Vjcm is applied to the in-flectors for a long enough time, the electrqn orbitshrinks gradually such as shown in Figure 4(Eo =-0.8 kVjcnl and'! = 9 n sec). This opera-tional condition is also beneficial for the captureof an electron beam of finite length.ACKNOWLEDGEMENTSThe authors wish to thank Professors A: Miyahara, G'.Horikoshi, K. Huke, S. Kawasaki and S. Usami for helpfuldiscussions. They also express their thanks to Professor 1.Alexeff for reading through the manuscript.REFERENCES1. A. Miyahara, S. Kawasaki, Y. Kubota, G. Horikoshi, H.Ishizuka, K. Huke, S. Usami, K. Akaishi and H. M. M.Saad, Tech. Rep. Inst. Plasma Phys., Nagoya Univ.,IPPJ-T-l1.2. H. Toyama, H. Toyosaka and K. Tsuda, Tech. Rep. Inst.Plasma Phys., Nagoya Univ., IPPJ-T-I0.Received 12 July 1973

Electron Orbits In The Era (electron Ring Accelerator) With an electrostatic-type Inflector System

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