Autoacceleration of high power electron beamsM. Friedman Citation: Applied Physics Letters 41, 419 (1982); doi: 10.1063/1.93557 View online: http://dx.doi.org/10.1063/1.93557 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/41/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Twocavity autoacceleration of an intense relativistic electron beam J. Appl. Phys. 61, 4760 (1987); 10.1063/1.338814 Radial electron beam autoaccelerator for inertial confinement fusion J. Appl. Phys. 55, 138 (1984); 10.1063/1.332877 Studies of the effects of a long pulse electron beam on the autoaccelerator J. Appl. Phys. 54, 6160 (1983); 10.1063/1.331930 Collective acceleration of electrons using an autoacceleration process J. Appl. Phys. 51, 6068 (1980); 10.1063/1.327639 Autoacceleration of intense electron beams by coaxial cavity structures Phys. Fluids 19, 1784 (1976); 10.1063/1.861375

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Autoacceleration of high power electron beams M. Friedman Plasma Physics Division, Naval Research Laboratory, Washington, D. C. 20375

(Received 19 April 1982; accepted for publication 22 June 1982)

The mutual interaction between a 70-kA intense relativistic electron beam and a passive structure increased the kinetic energy of electrons from 4.2 to 7.4 MeV. This process (known as autoacceleration) should be capable of generating electron beams with even higher particle energy and with currents> 100 kA.

PACS numbers: 41.80.Dd, 84.70. + p, 29.15. - n

The technology of generating intense relativistic elec­tron beams (IREB) is well developed l

-3 and is being used by

commercial companies.4 The price of an IREB generator depends on many factors one of which is the output voltage V. Information from commercial companies that make IREB generators shows that the price of generators of the same impedance and beam duration is proportional to va, anda> 3.

It was suggested that a potentially simple and inexpen­sive approach for generating a high-voltage IREB would be to use an autoacceleration process5

-8 on a lower voltage IREB. This process occurs during the mutual interaction between an IREB and a passive structure and leads to energy transfer from one part of the IREB to another part. In 1973, the principle of autoacceleration was tried experimentally. 6

It was shown that the second halfofa lO-kA, 0.5-MeV elec­tron beam gained energy to 1 MeV while the first halflost most of its energy. Since a I-MeV IREB can easily be gener­ated directly from a diode the autoacceleration process was not developed beyond the first preliminary experiment.

Renewed interest in generating IREB with kinetic ener­gy > 10 MeV, which is about the limit of a "conventional" diode, leads us to review this technique and investigate its potential. The theory of autoacceleration is given else­where. 5

,8 Here we give only a simple model relevant to this experiment [Figs. I(a) - I(e)]. An IREB of particle energy e Vo(t) [Fig. I(b)], current lo(t) [Fig. I(c)], and beam duration T, propagates through an evacuated drift tube. A coaxial cavity of impedance Z is connected to the drift tube via a gap. The length of the cavity is I = Tc/4 (c is the velocity oflight). A quasi-de magnetic field (Bz = 15 kG) guides the beam through the drift tube. As the IREB passes the gap, a current II(z,t) is induced in the cavity and a voltage VI(t) appears on the gap. II (z,t ) and VI (t ) can be calculated using transmission line theory. In particular the current at the end of the cavity is [Fig. I(c)]

II (/,t ) = 2/1(0,t) - 2IdO,t - T 12) + ... (1)

and the voltage VI that is developed across the gap is

VI(t) = Z [11(0,1) - 2/1(0,1 - T 12) + ... J , (2)

where II(O,t) = Io(t). For a square IREB current pulse, VI(I) has a bipolar form [Fig. I(d)]. Electrons lose kinetic energy eVI(I) per electron during the first half of the beam duration (0 < I < T 12) and gain the same amount of energy during the second half (T 12 < t < T)[Fig. 1 (e)].

In this letter we describe an experiment in which the autoacceleration process was tried on the highest voltage IREB generator available at the Naval Research Labora­tory, Washington, D. C. A 70-kA annular electron beam of 4.2-MeV energy was autoaccelerated to an energy of -7.4 MeV with no loss of beam current. The IREB diameter was - 4 cm, beam thickness - 2mm, drift tube diameter 4. 8 cm, and the cavity impedance Z = 45 fl. Figures 2(a) and 2(b) show oscilloscope traces of beam voltage and current. [The currents were measured by magnetic probes shown in Fig. I(a).] Using Eq. (1) and the measured beam current, Io(t) = II(O,t), one can calculate the cavity current, II(/,t). This can be compared with the measured cavity current [Figs. 2(c) and 2(d)]. Since the calculated and the measured cavity current are in good agreement there is a high degree of confidence in using Eq. (2) for calculating the gap voltage, VI(t ) and Vo(t) + VI(t) (Fig. 3). VI(t )ishard to measure direct­ly but can be qualitatively compared with the signal of an electrostatic probe (Fig. 3) located near the gap of the cavity. (The electrostatic probe is also influenced by the self-field of the beam and by particle and radiation bombardment.)

Three diagnostics were used to measure the electron

;-MAGNETIC PROBES? ;-BENDING p.-____ ----,/ / MAGNET ,GAP I

rD)~EB_-_-_-_--~>-" ------10 ¥V -H.V. / \. ( f\~l DE~E~~JR ~~6~~RIC - .-- I \ - " jl'l!.. ELECTRON

(a) ':{,AG~ET~; sFIE~D \'\' s , \_'COLL~:~~:OR COIL \.FARADAY CUP

O~ -V r-----'

(b) :

VIf]J; 0JTU/4 3T/

4;, 0 T ,

-V, :

-2I V2 (d) 0 (e)

FIG. 1. (a) Schematics of the experiment. (bHe) Ideal beam parameters for an autoacceleration experiment: (b) Voltage, (c) IREB current, (d) current at the end of the cavity, (e) voltage at the gap, and ( f) total voltage generated by an ideal autoacceleration experiment.

419 Appl. Phys. Lett. 41 (5), 1 September 1982 0003·6951/82/050419-03$01.0(\ © 1982 American Institute of Physics 419

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-lal 20 nsec

kA

140

120

100

80

60

40

20

o Id)

5 10

10

~I Ibl ~ 20 nsec

I,

~1 lei ~

10 nsec

15

nsec ~

FIG. 2. (aHc) Voltage, beam current, and cavity current in the present experiment. (d) Comparison between the calculated cavity current (solid line) and the measured cavity current (dotted line).

energy. It is known that the forward intensity E ofthe Brems­stralung radiation from an IREB of current I and voltage V is9

(3)

Figure 4(a) displays the signals of the forward x-ray intensity

MV. Vo

~L£:\ o 5 10 15 20 25 30 (a) nsec

V,

M.V.

~11 3

'2

<--->

0 20 nsec

-I

-2

-3

(b) VotV,

M.V.

7

6

4

r I r i

10 15 20 25 30 (e) nsec

FIG. 3. (a) Voltage ofiREB generator, (b) calculated vol­tage generated at the gap (shown in the insert is an elec­tric probe signal), and (c) elec­tron kinetic energy after au­toacceleration.

420 Appl. Phys. Lett., Vol. 41, No.5, 1 September 1982

X RAY

FARADAY ClW

< ) 20 ns

FIG. 4. X-ray and Faraday cup signals for the primary "non"-autoacceler­ated beam (left) and for an autoaccelerated beam (right).

of the autoaccelerated beam E I , and of the forward x-ray intensity of the primary 4.2-MeV IREB Eo. (The Bremsstra­lung from a carbon target was measured by a scintillator photo diode combination.) The current in the two cases was the same - 70 kA. From this measurement

(4)

Thus eVo(t) + eVI(t) = 1.8eVo(t )~7.5 MeV. Note that the duration of the x-ray pulse is only 10 ns for the autoacceler­ated beam while the duration of the primary 4.2-MeV beam is 20 ns.

Another way to determine electron kinetic energy was to pass some of the beam (- 3 kA) through different thick­ness of carbon discs and to measure the transmitted current with a Faraday cup. The range of 4.2-MeV electron in car­bon is 2.1 g/cm2. At this thickness the Faraday cup gave a signal shown in Fig. 4(b)-left for the transmitted primary 4.2-MeV IREB. To obtain a similar signal level with the autoaccelerated beam required -3.8 g/cm2, [Fig. 4(b)­right). Since the ratio of the two ranges is equal to the ratio of the energies of the two beams,1O the energy of the autoacce­lerated beam determined by this method is 7.5 MeV.

A direct way to measure electron kinetic energy is to measure radius of curvature of electron trajectories in a transverse magnetic field. In the experiment a small fraction of the electrons that emerged outside of the axial magnetic field were collected and collimated into a bending magnet [Fig. l(a)]. It was found that the highest electron energy was - 7.9 Me V and that most of the electrons were with energies between 6.1-7.5 MeV (Fig. 5). The electrons were detected by a scintillator photodiode combination [Fig. l(a)).

M. Friedman 420

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E 20 ns )

FIG. 5. Signal from an electron detector. A transverse magnetic field was used to select only elec­trons with energy between 6.1-7.5 MeV.

To estimate the limits of the autoacceleration process, one has to ask: (1) What is the maximum current that can propagate inside the cavity? (2) Whit is the highest electric field that the gap can sustain?

(1) The current that can propagate inside the cavity is

10 S. Ie (kA ) = 17(y2/3 - W/2 F(G), (5)

where F(G) is a function of the geometry (Ie is the critical current and in the experiment Ie ::::: 200 kA).

Once the geometry was chosen the only increase in cur­rent can come with a proportional increase in beam energy, i.e., Vol 10 = constant. In that case the relative increase in beam voltage due to the autoacceleration mechanisms will be

VJVo=Io Z IVo = constant, (6)

where Z is the impedance of the cavity. (2) The voltage at the gap is limited by parasitic current

initiated by negative electric field at the metallic surfaces of the cavity and the gap. The electric field is the sum of the induced electric field E; and the space-charge electric field Es' E; and Es are both proportional to beam current and from Eq. (6) E;I Es = constant. In order to prevent parasitic current to flow across the cavity and the gap E; + Es > - 500 kV Icm (Ref. 11) at any metallic surface. In the

421 Appl. Phys. Lett., Vol. 41, No.5, 1 September 1982

experiment described here, the electric field in the cavity (including the gap) was calculated by solving Maxwell's equations for the geometry shown in Fig. l(a) and for 10 = 75 kA. It was found that: (1) The electric field inside the cavity is large enough ( ~ 2 MV I cm) to cause electron emission. How­ever, the strong quasi-dc magnetic field quenches the para­sitic current. (2) The electric field on the metallic surfaces at the vicinity of the gap is strongly influenced by the space charge of the beam to the extent that E; + Es > 0 for any current level. (3) Regions where E; + Es < 0 and where there was no magnetic insulation the geometry of the cavity could be modified to keep E; + Es > - 300 k V I cm and hence pre­vent parasitic current. Doubling beam current with some change in cavity geometry (e.g., gap length) keeps this pic­ture unchanged.

In conclusion it was shown that the autoacceleration technique is capable of generating high power IREB with high particle energy. Doubling the primary beam voltage and current (in comparison with present experiment) and using the autoacceleration technique will generate an IREB with kinetic energy of > 15 MeV. This beam is difficult to generate by conventional means.

The author gratefully acknowledges Dr. A. E. Robson, Dr. P. Avivi, and Dr. V Serlin for their helpful discussions and Mr. F. Klaiber and Mr. L. Daniels for their technical assistance.

IT. C. Martin, V. S. Patent No.3 344 298 (26 September 1967). 2S. F. Graybill and S. V. Nablo, Appl. Phys. Lett. 8, 18 (1968). 31.1. Clark, M. Vry, M. L. Andrews, D. Hammer, and S. Linke, in Record a/the 10th Symp. a/Electron. Ion. and Laser Beam Technology, edited by L. Marton (San Francisco, San Francisco, 1969).

'For example, Physics International and Maxwell Laboratories. sL. N. Kazanskii, A. V. Klestov, and A. N. Lebedev, At. Energ. 30, 27 (1971).

6M. Friedman, Phys. Rev. Lett. 31, 1107 (1973). 71. A. Grishaev and A. M. Shendorovich, Sov. Phys. Tech. Phys. 17, 1871 (1973).

81. Siambis, Phys. Fluids 19, 1784 (1976). 9H. W. Koch and 1. W. Motz, Rev. Mod. Phys. 31, 4 (1959). IOFor example, R. D. Evans, in The Atomic Nucleus (McGraw-Hili, New

York, 1965), p. 625. 110. Conte (private communication, 1979). Experiments were performed at

NRL using the Gamble 1 facility to find what is the electric field intensity needed for explosive emission of electrons from metallic surfaces.

M. Friedman 421

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