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ROA-RIB5 683 MODULATION OF AN INTENSE BERM BY AN EXTERNAL MICROWAVE 1I/0y SOURCE - THEORY AND SIMULATION(U) NAYAL RESEARCH LABI HASHINGTON DC J KRALL ET AL. B? OCT B? NRL-MR-6SB3
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NRL Memorandum Report 6083
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Modulation of an Intense Beam by an ExternalMicrowave Source - Theory and Simulation
J. KRALL* AND Y. Y. LAU
Plasma Theory BranchPlasma Physics Division
*Science Applications Intl. Corp.
October 7, 1987
DTICS ELECT-
NOV 0 5 1987 D
Approved for public release; distribution unlimited.
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11. TITLE (include Security Classification)Modulation of an Intense Beam by an External Microwave Source-Theory and Simulation
12 PERSONAL AUTHOR(S)Krall* J. and Lau, Y.Y.
13a TYPE OF REPORT 13b TIME COVERED 14, DATE OF REPORT (Year, Month, Day) IS PAGE COUNTInterim FROM TO 1987 October 7 18
16 SUPPLEMENTARY NOTATION
*Science Applications Intl. Corp.
17 COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and Identify by block number)
FIELD GROUP SUB-GROUP .*Current modulation , Intense relativistic electron beam
, I Highpower T amplifier
19 ABSTRACT (Continue on reverse if necessary and identiy by block number)
A time dependent, fully electromagnetic particle code is used to simulate the current modulation in an intense rela-tivistic electron beam (IREB) by an external rf source. It is shown that the intense beam may serve as a power amplifierwith good phase stability, as suggested in earlier experiments. Increase in beam bunching by the DC space charge isdemonstrated with a simple analytical model. / ,
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Y.Y. Lau (202) 767-2765 Code 4790DO Form 1473. JUN 86 Previous editions are obsolete SECURITY CLASSIFICATION OF THIS PAGE
U % tttt,:ab..XL'*'r.C SC- .Y tt * '- ; tA Ce,% t .;. .. .
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Modulation of an Intense Beam by an ExternalMicrowave Source-Theory and Simulation
The experimental demonstration of deep current modulation in an
intense relativistic electron beam (- 5 kA, 500 keV) by a moderate external
rf source (- 50 kW) suggests strong potentials2'3 to amplify rf power to
gigawatts at frequencies between 1 GHz to 10 GHz. Several unusual
properties were discovered in the experiments 1 4 , namely, the high degree
of phase and amplitude stability in the output signal1 , the ease with which
the current modulation can be achieved and may be manipulated by the
introduction of additional, undriven cavities downstream, and the possible
avoidance of electrical breakdown at the gaps even at a high level of beam
modulation5 . These unexpected features are only partially understood. The
major obstacle to a complete understanding is the highly nonlinear
interaction in complex geometries involving the kinetic energy, rf energy,
and the potential energy of the beam, all of which are of the same order of
magnitude. The crucial role played by the potential energy, which
necessarily accompanies an intense beam, renders the classical picture of
beam bunching invalid.
We, therefore, resort to a time dependent, two-dimensional, fully
electromagnetic particle code, CONDOR6 , to simulate the response of an
intense beam to an external rf excitation. This amplifier configuration
has never been subject to particle simulation, although self-excited
7oscillations have been studied in the past . We found that when the
external rf drive is low, the induced rf current agrees well with the small
1,7signal theory . Addition of a second cavity in the drift region
significantly enhances the current modulation, without loss of phase
stability, as observed in earlier experiments 1. An analytical model is
presented to show that the DC space charges associated with the intense
beam may encourage current bunching as the beam traverses a modulating gap.
Manuscript approved Jy 24, 1987.
The harmonic content is assessed. The details, together with experimental
4observations, will be published elsewhere
To mimic the experiments as closely as possible, the simulation
geometry [Fig. 11 consists of a 500 keV, annular IREB with beam radius
rb - 1.9 cm and beam current I° = 5 kA propagating along a metal cylinder
of radius r = 2.4 cm. A static 10 kG axial magnetic field confines the
IREB. A gap feeding a coaxial cavity 5.6 cm long is inserted into the
drift tube. An infinite radial transmission line (not shown) is attached
to the outer wall of this cavity and "pumps" rf energy into the cavity at a
frequency f = 1.37 GHz, the resonsance frequency of the cavity. At t = 0,
the rf drive is turned on. At t = 6 ns, after the fundamental mode of the
cavity has saturated, the beam current is ramped up, reaching its full
value at t = 11 ns (5 ns rise). The simulation continues until t = 20 ns.
For rf drives yielding gap voltages with amplitude V 1 = 30 kV and
V1 = 6 kV, the axial distribution of the normalized rf current 11 Cz)/I ° in
steady state is shown in Fig. 2. The temporal evolution of the beam
current at a distance z = 28 cm from the gap center is shown in Fig. 3a for
the V1 = 30 keV case.
The above results may be compared with linear theory7 ,l: An rf
voltage VIsinwt at the gap would induce an rf current 11(z)cos(W(t-z/v0 ))
at a position z downstream, where
11 (z) = I V sin z (1)
Here, v is the average electron speed in the drift region 8 , V = (eV1/MC
2
/(y 0o2o/ 0 = 2n(z/X)a 1/2/3o2YO , 6 = 2 2 - ),c = Io/IsYo3 0 ,
I s = 8.53 kA/ln(rw/rb), X=2nc/w, 0=vo/c, yo=(y0o1) - 0 The axial
dependence 11(z)/l 0 according to expression (1) is shown by the dashed
curves in Fig. 2, using the same parameters as in the simulation: I =
5kA, X = 21.9 cm, Is = 36.5 kA, Yo 1.67. Note that Eq. (1) and Fig. 2
2
J. '. -. . .o " r r r -
imply linear dependence of 11 on V1 when V1 is small. As V1 increases, the
current modulation would contain harmonic components In (z) a 2 IoJ n
(n Vsinz) where Jn is the Bessel function of order n. This estimate shows
that only the fundamental component (n=l) is significant if 7 < 0.3.
To obtain a current modulation comparable to 10, V1 should also be of
the same order of the beam voltage. It is impractical to excite such a
large gap voltage directly from an external rf source. Instead, one may
insert a second cavity downstream [Fig. Ib], at a location where the
current modulation (by the first cavity) reaches a maximum1 . This second
cavity is identical to the first, but is not externally driven. Using the
same rf drive as that for Fig. 3a, we show in Fig. 3b the temporal
evolution of the beam current at 6 cm downstream from the second gap, at
which the gap voltage is 330 keV. The total current modulation thire
increases to 57%, including all harmonics. In fact, the modulation level
continues to increase over the remaining 10 cm of propagation distance,
reaching 85%. No particle reflections were observed at the second gap, nor
transients were important. These results compare favorably to both the
experimental two-cavity result, in which the cavity separation was 5 cm and
modulation greater than 80% was observed at 1.328 GHz1 , and to more recent4
results in which the separation is 32 cm4. In this situation, the harmonic
content is considerable, with as many as eleven harmonics clearly
observable in the current measured immediately downstream from the second
gap.
Substantial current modulation immediately beyond a gap is a property
of an intense beam which cannot be expected from the conventional klystron
theory. While the details are not fully understood, the following scenario5
emerges : When the beam current 10 approaches the limiting value, IL? the
3
"- • , , .'? "':%
DC potential energy is nontrivial, especially near the gap. If the
modulating voltage V1 at the gap is sufficiently large, the instantaneous
beam current may exceed the limiting value during the part of the rf cycle
when the rf voltage is in the same phase as the retarding voltage caused by
the DC self field of the beam. This then leads to strong current
modulation once the beam exits the gap. In a simple model, the current
modulation 11/10 at the gap exit reads:
ti1 0) e m (i - Vth /Vl (2)
where the threshold voltage Vth is given by
Vth = 0c2 l - 2/1 (inj 2/3 _ ')1 2} (3
in terms of the injection y and the limiting current IL . This current
modulation is absent if V1 < Vth, but rises rapidly once V1 > Vth, and
becomes insensitive to V1 if the latter substantially exceeds Vth [c.f. Eq.
(2)]. These features are also reflected qualitatively in experiments.
Finally, by varying the phase of the external rf drive in the two-
cavity geometry [Fig. ib], we have found that the current modulation signal
is phase-locked to the external drive to within an error of 1.1 ± .6%, in
agreement with the experimental observation1 .
In summary, several unusual features observed in experiments on the
modulation of an intense beam are confirmed in the particle simulation.Useful analytic models are constructed.
We are grateful to M. Friedman and V. Serlin for many stimulating
discussions, and for their support. We are also indebted to Scott Brandonand to Adam Drobot for their assistance in applying CONDOR6 to this
problem. This work is supported by the Department of Energy, Contract No.
DE-AI05-86 ER 13585.
4
References
1. M. Friedman and V. Serlin, Phys. Rev. Lett. 55, 2860 (1985).
2. M. Friedman and V. Serlin, Appl. Phys. Lett. 49, 596 (1986).
3. M. Friedman, V. Serlin, A. Drobot and A. Mondelli, IEEE Trans., Plasma
Sci., PS-14, 201 (1986).
4. M. Friedman, V. Serlin, J. Krall and Y. Y. Lau, submitted to Phys.
Fluids.
5. M. Friedman and V. Serlin, private communication.
6. CONDOR is an extension of the MASK particle code, discussed in A.
Palevsky and A. Drobot, "Application of E-M P.I.C. codes to microwave
devices," in Proc. 9th Conf. Numerical Simulation of Plasmas
(Northwestern Univ., Evanston, IL), July 1980 (unpublished).
7. M. Friedman, V. Serlin, A. Drobot and L. Seftor, Phys. Rev. Lett. 50,
1922 (1983); Also J. Appl. Phys. 56, 2459 (1984).
8. Since the electrons already spend some energy to set up the space
charge depression in the drift region, their drift speed u° is
somewhat less than the value at injection.
Accession For
NTIS GRA&IDTIC TABUnannounced 0Justification
/ By
Distribution/
Availability Codes'Xv::[1 and/or
As NSPEcTED
L6
5
~rf DRIVE
6-
"9° 4L. (a)
2
0i
0 10 20 30/ 40 50
INTENSE E-BEAM
frf DRIVE
6 .
(b)2
0 10 20 30 40 50
CENTER AXIS (cm)Fig. 1 (a) The geometry. Current modulation is provided by the
externally driven cavity at left.
(b) A second cavity is inserted to enhance current modulation.
6 ,
0.15- 1 V1 =30kW
0.10-
SIMULATION
ANALYTICAL
0.05-
V1 =6kW
o0 10 20 30 40 50z (CM)
Fig. 2 Fraction of the modulated current for Fig. la, at two
levels of the rf drive.
7
N,.~ . .
0.0
1.5-
3.0- -(a)
4.5-
6.00 4 8 12 16 20
t (ns)
0
3
II (b)" 6"
9
12 * - -
0 4 8 12 16 20t (ns)
Fig. 3 (a) Current response measured at z = 28 cm from the gap for
Fig. la, with gap voltage V1 = 30 kV.
(b) Current response measured at 6 cm downstream of the second
(right) cavity in Fig. lb, with V1 = 30 kV at the first
cavity.
8
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