The 9th Symposium on Accelerator Science and Technology, Tsukuba, Japan1993

Electron Linear Accelerator based onVp x B Acceleration Mechanismusing Disk - Loaded Slow Wave Structure
Hirornitsu Inoue, Noboru Yugami and Yasushi Nishida
Department of Electrical and Electronic Engineering,
Utsunomiya University,
2753 Ishii-machi, Utsunorniya, Tochigi 321.

Abstract

Theory ofv;, x B Accelerationv;, x B acceleration, which has been

We consider the motion of a charged particle in the lab-demonstrated by using a square shaped slow wave structure,oratory frame of reference( Fig. I). The static magnetic fieldt - 3 ) higher acceeleration rate compared with a conventional

is applied in the x direction. An electromagnetic field propa-electron linear accelerator. In the present experiments a disk

gates in the z direction. The present electromagnetic wave is- loaded slow wave structure is employed for demonstrating

TM mode, which has a longitudinal component of the wave

this mechanism. The incident electron beam velocity is about

electric field.

The mechanism ofThe motion of charged particle can be written in the0.43c (corresponding to 50 keV). The energy increment of theelectron is proportional to the square of the applied magnetic

frame moving with a phase velocity vp (wave frame).

field until the paarticle trapping condition breaks, in reason-(I)

able agreements with the theory.

Introductiond(fV.)
mo--;rr- = qEosm KZ - qBolpVy,
0()

(2)

Recent particle accelerators require a tremendously large
appratus in order to obtain fully accelerated high - energy

where the capital letters denote the values measured in theparticles.

wave frame and r = (I - V2 /c2The particle accelerators demand new accelera-tion principles that can create a high field gradient . Several

kf'yp , and IP = (I - v;/c2

new acceleration shemes, specifically using plasma, includ-In eq.(2),ift 112 , V2 = V,.2 + V,} , K =t 1

1 2 •ing a plasma wake field accelerator (PWFA), a plasma beat(3)

wave accelerator (PBWA) and a V, x B accelerator, have been
is satisfied, the particles are kept accelerating. This is ·theproposed. 4 -n)
In this paper, we report experimental results on the elec-trapping condition of the particle in the V, x B acceleration

tron linear accelerator based on new type particle acceleration

scheme.

scheme, which is called the V, x B acceleration scheme, or theThe total energy of the electron 1 is written as

Cross Field Accelerator (CFA). The V, x B acceleration phe-(4)nomena have been observed in the experiments of microwave- plasma interaction for the first time.

10In this scheme aor

static magnetic field is applied vertically to the wave propagating direction and the particles are accelerated continiously(5)
The increment of 1 in y and z direction arealong the wave front at constant phase with respect to thewave, until the trapping condition breaks. In this scheme, thedriver wave should be a longitudinal mode, but the transverse

d1 _ WcVpl~
dy-~

(6)

dl
w2 [w2 ] -1/2
wc__£,
c 2""'-~
dz - 1 c2 z I + -;?z~ lp-;;·

(7)

--

wave could also be employed.

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Thus, in the limit vP --+ c, the increment in the y direction is/p times larger than in the z direction, i.e.

Experimental Resultsthe Vp X B accel-Figure 3 shows the energy increment as a function of theeration has larger degree of acceleration compared with theincident electron energy varied from 10 to 60 keY. Symbol<>,

conventional acceleration scheme.

D , andX

Detrapping

is 0, 0.33, and 0.5 Gauss, respectivily. Three acceleration

Acceleration/

0 denote the results when the applied magnetic fieldregions appeared. Typical examples of the observed energy
spectrum with the change of the applied magnetic field are

Ez =Eo sin(kz - cot)shown in Fig.4 , where the incident beam energy is 42 keY.
At B = 0 , the accelerator operates again as the conventional electron accelerator. Until B = 1.1 G , the electronzyenergy corresponding to the peak flux indicated by an arrow
Trapping Condition

increases. For further increase after B = l.lG , the decrease

Eo> YrSrY yof electron energy was observed. This shows that the magnetic

Figure 1

field strength B = 1.1 G is a critical value for the trapping
condition. Detailed discussion will be presented later on Fig.5

Experimental Apparatus
Figure 2 shows the experimental apparatus. The electron
gun for the electron beam injection has a maximum energy of
100 keY with a maximum beam current of 1.5mA. The accelerated electrons through the accelerator are analyzed by theelectron energy analyzer, and are detected by an MCP(microshows the relation between the applied magnetic field and theenergy increment tlt: . Where the incident electron beam energy is 42 keY in Fig.5 . Solid line represents that !::.~::' which
is proportional to B 2 • This dependence will be discussed inthe next section.

7channel plate) detector.
The RF source is a magnetron of 2.45 GHz with a typical

65pulse width of 10 psec in repetition of 10Hz. The maximum

4power is 10 kW. A vertical magnetic field in the x directions
is produced by a pair of saddle - shaped coils. The maximum
strength of the applied static magnetic field is 10 Gauss. The
present experimental apparatus can be operated as a conven-i!

a1\1ll g

3\2
1~

0-1-2

er~
~~
11.100,nIf_40-oG- o - 0.33G-o.sG

50 55 60 65

tional linear accelerator, when no magnetic field is applied.

35

Therefore, we can easily demonstrate both the Yp x B accel-Incident beam energy (keV)

45

Figure 3

eration and the conventional linear accelerator.
Dummy
Load~

1.9 Gauss
1.5 Gauss
1.2Gauss~~

1.1 Gauss

E, =42 keV

O.B Gauss
0 Gauss
RFOFF
Flux

Figure 2

Figure 4-340-

L
EnergyInserting experimental values, the caluculated td , T , Ed are10

listed in table 1. Symbole T represents the time when theII

1electron travels through the accelerator with the incident velocity. Where T is the transit time of electrons with an initial
velocity, E is the electric field in the accelerator, and Ed is a"•~ 0.1value of magnetic field for td = T • The table 1 shows td ~ Tand E ~ Ed. Thus, the experimental results can be compared70.010.01

with the theory.
Conclusion

1010.1The v;, x E acceleration scheme are demonstrated in a

B (Gauss)

disk - loaded electron linear accelerator. The energy gain(~c;') for Vp x E acceleration is proportional to E 2 , and isFigure 5

in fairly good agreement with the theory. When the incident
Discussion

beam energy is 42 keV, the electron is detrapped from theIn eq. (5), 1( z) expresses the total energy of the electron.

wave trough at E = 1.1 (Gauss), and showing the coinci-

The energy gain(tq = 1(z)- {p) is given bydence with the theoretical value.

~~ = ~ (w;zrReference

(8)

[1]
Therefore, we obtain

Y. Nishida and R. Sugihara, Laser Interaction andRelated Plasma Phenomena vol. 7(Plenum, New York, 1986) Chap.9 p.803.

(9)
[2]

This equation shows that ~£' is proportional to E 2 • The

Y. Nishida and H. Onihashi, Proc. 6th Sympo. onAccel. Sci. and Tech.,Oct 27-29 1987, Tokyo, p.183.

experimental results are in fairly good agreements with the[3]theory.

Y. Nishida, N. Yugami, H. Onihashi, T. Taura andK. Otsuka,Phys. Rev. Lett. 66, 1854- 1857, (1991 ).

We consider the trapping time of electrons. If td is the[4]time when the electron is detrapped from the wave trough,Y. Nishida, High Energy Particle Accelerators
by Laser, INOICS (1986).

we have[5](10)T. Tajima and J. M. Dawson, Phys. Rev. Lett.
43 (1979) 267.

where 8 = w:fwl ~ 1, We= qEjm, and wl = qEkjm. In theexperiment, we assume that z(O) = 0, vy(O) = 0, at t = 0,then we obtain,[6]

P. Chen, J. M. Dawson, R. W. Huff, andT. Katsouleas, Phys. Rev. Lett. 54 693 (1985).

[7]

J. B. Rosenzweig, D. B. Cline, B. Cole, H. Figueroa,W. Gai, R. Konecny, J. Norem, P. Schoesson, and(11)J. Simpson, Phys. Rev. Lett. 61, 98 (1988).

[8]

Since 8 ~ 1, we have

H. Nakanishi, A. Enomoto, K. Nakajima, A. Ogata,
T.Urano, Y. Nishida, S. Ohsawa, T. Oogoe, and(12)E(kVjm)mE
kmE
td = qwcb2 = qcE 2 = 1. 90 E 2 (Gauss)(ns)

H. Kobayashi, Particle Accelerators,

32, 1645 (1989).

(13)
[9]

47 (1979) 1290.

Table 1 The parameters of the experimental results and td
E (kV/m)
3.2

B (Gauss) td (ns)
1.1

4.95

T(ns)

Ed (Gauss)

4.18

1.21

R. Sugihara andY. Midzuno, J. Phys. Soc. Japan[10]

Y. Nishida, M. Yoshizumi, and R. Sugihara,Phys. Lett. 105A, 300 (1984).

[11]

T. Katsouleas and J. M. Dawson, Phys. Rev. Lett.
51, 392 (1983).

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