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NATIONAL BUREAU OF STANDARDS -1963
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A METHOD FOR INTRODUCING ENERGY SPREAD IN INJECTION MACHINES*
Randall S. Edwards and Herman Postma
NOV 2 9 1966
CONF-661016-29 ...
A.C. $ 400 min 5

1.
INTRODUCTION
DCX-i is a dc experiment at Oak Ridge which accumulates a plasma by injection
and dissociation of high-energy H,* ions in a simple magnetic mirror geometry.
The principle by which DCX-1 operates has been described in previcus articles,'-5
but will be repeated in abbreviated form for completeness. Figure 1 is a schematic
sketch of DCX-1. The H * ions are produced in a duoplasmatron ion source, accel-
erated to 600 key by a cascade transformer power supply, focused and then deflected
so that they enter a 10-kilogauss confining magnetic field midway between t} 2:1
mirror coils. The ions make a single pass in the midplane and exit through the
bottom of the vacuum chamber. In the process of making this single pass some of
the ions dissociate to yield protons and hydrogen atoms. Those protons which re-
sult from this dissociation in a region near the 3.25-in. equilibriun radius are
Change
trapped by means of their e/m change and continue to circulate with a gytofrequency ,
of approximately 15 MHz. when the molecular ion beam is injected, the density of
the circulating protons increases until the trapping rate is equal to the loss rate.
The loss of protons from the plasma is the result of either charge exchange with
background gas or instabilities generated in the plasma region. In DCX-1, micro-
instabilities limit the maximum trapped proton densities to 1 x 10° cm which is
a factor of 50 below that theoretically possible with the available beam and
pressure. 6,7
Since theory suggests that certain microinstabilities are suppressed by
the introduction of sufficient spread in the energy distribution of the trapped ::
ions, we have developed a practical method of introducing such spread. In this
Research sponsored by the U. S. Atomic Energy Commission
under contract with the Union Carbide Corporation.

AELEASED FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS
ATS
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paper we present the considerations which led to the choice of this particular
method, establish design criteria for the apparatus, describe in scme detail the
equipment developed for this purpose, and review briefly the performance of this
equipment when applied to the plasma of the DCX-1 experiment.
.
.
.
i
.
.
.
.
II. CHOICE OF METHOD
Two general approaches to the problem were recognized. Energy spread could
be introduced by modulation of the 600-kv supply furnishing the acceleration
potential for the Ho* beam, or it could be introduced by using external sources
to produce proton-electric field encounters within the plasma itself. The H,
beam trajectory changes associated with modulation of beam energy would not permit
obtaining the desired proton energy spread, a value at times in excess of 50 ker ,
U
L
J.
as suggested by some experimental studies of the unstable plasma. Therefore,
attention was focused upon the second approach.
• We decided to employ a dispers.ng technique patterned after that used in
synchrocyclotrons to give spatial and energy dispersion of extracted beams.
The technique is to nount cyclotron dee structures so as to encompass the circu-
lating protons, and to drive these structures with a noise band centered about
the proton gyrofrequency. This arrangement produces stochastic acceleration of
the circulating protons and thereby creates the desired energy spread.
III. DESIGN CRITERIA
We shall give an expression for the induced proton energy spread as a function
of dee voltage, dee signal bandwidth, interaction time, and e, the azimuthal angle
subtended by the driven dee. We assume the simplest proton distribution that can
exist in DCX-1, a ring of 300-kev protons çirculating about the magnetic axis at
the ion gyrofrequency of 15 MHz, and we subject this ring to the stochastic
LEGAL NOTICE
.....common.....
The report was prepared as an account of Government sponsorod work. Noither the United
States, nor the Commission, nor any person aquing on behalf of the Commission:
A. Makos any warranty or representation, express or implied, with respect to the acou-
racy, completeness, or usohulnods of the information contained in this rorort, oi that the wo
of any information, apparatus, molhod, or procoas disclosed in this soport may not Infringo
privately owned righta; or. 1:
B, Assumes any liabilites with roupoot to the use of, or for datingos resulting from the
use of any information, Appuritus, method, or process dooloved in this report.
As und in the abovo, "person 'holing on behalf of the Commission" includne any nm-
ploys or contractor of the Commission, or employs of such contractor, to the extent that
suok omployer or contractor of the Commission, or employee of such contrroter preparos,
disseminates, or provides aocons do, any information purdunat to do employment or oontract
with the Commission, or his employment with such contractor.
.
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variations of electric field introduced by a 180° dee structure driven by a
band of frequencies centered on the gyrofrequency.
The change in energy, E, due to random interactions is expressed by:
(1)
i=1
where E“ is the total mean square change, N is the number of independent inter-
2
actions and E. is the mean square change of energy during a single interaction.
Simplified into the more common form in which averages are implied, we have:
E - VN
;
(2)
We now apply this general form to our particular situation. At the dee
structure, we create a randomly varying voltage V such that E, equals ev..
We can do this in principle by making the voltage vary at random in phase,
frequency or amplitude. If we assume further that the particle remains in
resonance for the time between phase changes, then in this time it acquires an
energy of:
e = eveff 2 sin
,
.
(3)
where Veff is the effective dee voltage (which depends on when the particle
entered the dee with respect to the voltage peak, whether an acceleration or
deceleration cycle, gap width, etc.); T is the average time of a phase change
for acceleration or deceleration cycle; 2 sin is the effectiveness of the
dee in acceleration where is the azimuthal extent of the dee and T. is the
revolution time of the proton. It follows from these definitions that the
number of random interactions during a time T is: .
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Combining these relations we express the energy spread in terms of the experi-
mentally variable factors:
V
eVoff 2 sin .
(5)
In order to see the rate at which one wishes to spread the ion energy we must
turn to past observations. For example, in the region in which the instabili.- . .
ties are at their worst we have several-second containment times. The best
indications of the instabilities are the azimuthal currents of protons measured
as rf signals, that give almost periodic bursts of rf at gyration frequencies
and cause a radiai loss of protons at the same time. Burst durations of 10 msec.
out of a total of 100 msec are typical. In the intervening time the plasma is
very quiet and stability seems to be present temporarily. The er argy spread of
the particles is normally between 50 and 100 keV in this mode. Other experiments
have shown that it is those well-ordered particles in the simple equilibrium orbit
ring that we have assumed, that are the most effective in causing the instability.
Thus the experiments themselves suggested that if we affect those particles which
are in this simple ring and that if we spread the energy on the order of 50 keV
within times that are much shorter than 100 msec, then we can possibly cure the
instability.
Thus we do a simple calculation to see if this is feasible. We shall assume
0 = 180° (normal cyclotron dee shape), T = 10 msec, 7. = 7 x 10** sec, and a band-
width.corresponding to 10-0 sec between phase changes. This bandwidth selection
arises from other considerations to be given later. Thus to get a spread of 50 kev
from formula (5) the effective voltage need be only 17 volts. Thus we see that the
kinds of voltages and bandwidths that we are asking for are very reasonable.
Other conjectures about this simple system may also be made. For instance, phase
.
bunching of this ring takes place due to the presence of the dee. The number of
bunches depends directly upon the bandwidth. It is desirable to have a large
number of bunches from a plasma point of view. Thus a practical compromise
between heating the particles rapidly with small voltages, such as might be
achieved by resonance, or between making many bunches which is desirable from
a plasma point of view leads one to regard the assumed 1 MHz bandwidth as being
practical. Phase changes that a particle sees in going between gaps, the focusing
and defocusing by the dee gaps themselves, and practical considerations of the
dee-gap construction do not significantly modify our initial assumptions. Also
it is possible to use such a stochastic system with dees not only at the funda-
mental but at 45 MHz. "It is also possible to use a 15-Miz drive without a dee
structure by means of just a simple plate, a cee structure. However, we have
chosen here to describe the simplest system, although in practice we have used
two structures. One, the simple dec structure shown in Fig. 2, is most suited
for operation at the third harmonic of the proton gyrofrequency. This frequency
was chosen because it interferred the least with the diagnostic measurements that
we make of the instability appearing as rf burst at 15 MHz. However, in order to
prove the effectiveness of the method and also to allow the plasma more room
a.jally, we later used a cee structure without sidewalls, shown in Fig. 3, driven
at 15 MHz.
IV. DESCRIPTION OF EQUIPMENT
The more complicated accelerating structure was that for operation at
45 MHz, the third harmonic of the proton gyrofrequency. At this frequency
both driven and passive elements were necessary, and side walls were required.
The details of this dee structure are shown in Fig. 2. The allowed radial
extent of the piasma was 9 in., and the allowed axial extent was 1 and 1/2 in.
.
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The accelerating structure for operution at 15 MHz, the fundamental fre-
quency, required only a driven element without the side walls, as shown in Fig. 3.
The allowed radial extent of the piasma was again 9 in., but the allowed axial
extent was increased to 6 and 1/2 in.
A block diagram of the electronic systems for 15 MHz and 45 MHz drives
is provided as Fig. 4. The elements comaon to both systems were the noise
source and its associated wide-band amplifier. The noise source, Fig. 5, con-
sisted of a 1P28 photomultiplier tube illuminated by a variable intensity light
source. Adjustment of the light intensity and the anode voltage of the photo-
multiplier tube gave excellent control of nois: signal amplitude and some con-
trol over the frequency distribution. Use of a spectrum analyzer showed that
the amplified noise from the Hewlett-Packard 461 wide-band amplifier was of
essentially constant level for bands several MHz wide centered on the funda-
mental and on the third harmonic.
The driver and intermediate-level amplifiers for both frequency ranges
were designed and constructed in-house. Maximum flexibility in the use of
these units was desired, and for this reason the amplifiers were built as inde-
pendent modules.
Figure 6 is a schematic of the 15-MHz driver amplifier, and Fig. 7 is a
schematic of the 45-MHz unit. The 2526 vacuum tubes were selected because of
their low drive requirements. Over-coupling and double-link coupling were used
to flatten the frequency response. No unusual problems were encountered in the
design or layout of these units.
Figure 8 is a schematic of the 15-MHz intermediate-level power amplifier,
and Fig. 9 is a schematic of the corresponding 45-MHz amplifier. These units
provided the outputs of approximat:oly 100 watts that were required to drive the
.
.
.
.
.
.
...
.
.
.
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.
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final power amplifiers. The requirements for fast gating of the voltage to the
dee structure were met by providing external access to the control grids of the
input stages of these amplifiers. The dee voltages were reduced to an extremely
low level by applying to these terminals a negative pulse from an external
programmable source. This gate was necessary to permit diagnostic measurements.
The final amplifier for the 15-MHz system was a standard Telonic Corporation
Model 2000. This unit was fixed tuned with input and output impedances of 50 ohms,
and was capable of a 600-w output with a bandwidth of 2-30 MHz.
The final amplifier for the 45-MHz system was basically a Telonic Corporation
Model 2000, but was factory modified for operation at 45 MHz with a 3-MHz band-
width and was capabie of 450 w output.
Amplifier connection to the dee structure in each case was made through a
RG8/U coaxial cable which was cut and tuned to give maximum voltage at the dee.
The coaxial feed-through through the wall of the vacuum chamber to the dee was
made by means of a specially constructed matching section of coaxial copper tubes.
In operation, a system was initially tuned by using a sweep-signal generator
and a spectrum analyzer, first across each of the amplifiers and then across the
whole set of driver, interrediate, and final amplifiers. Final tuning employed
the noise signal and the spectrum analyzer, and was a matter of minor adjustment
to obtain the desired spectrum on the dee itself. The flexibility of the system
gave a number of controls on the dee voltage level.
v. PERFORMANCE
The amplifier systems met the design specifications in all respects. The
bandwidth was flat over more than 3 MHz at both 15 and 45 MHz. At the dee
structures, up to 800 v were obtainable with the 45-MHz system and up to 1500 v
****
SYAF RU7011
with the 15 MHz system. These voltages were considerably in excess of those
actually required for the plasma experiments, the latter usually being 150 v
or less. The energy spreads were controllable, and in some experiments spreads
as large as 140 kev FWHM about the normal 300-kev proton energy were introduced.
The details of the plasma experiments involving measurements of micro-
instability thresholds as a function of energy spread obtained by the technique
described here have been reported elsewhere. 9,10 The technique has proven to be
a valuable diagnostic tool, and assisted greatly in establishing the negative-
mass instability as that dominating the DCX-1.plasma. A similar technique has
recently been employed in the PHOENIX experiments."
VI. ACKNOWLEDGMENTS
We wish to thank other members of the DCX-1 group, namely, J. L. Dunlap,
G. R. Haste, L. A. Massengill, R. G. Reinhardt, W. J. Schill, and E. R. Wells
for their contributions in the development and understanding of the apparatus.
Thanks are also given to J. A. Martin, of the Electronuclear Division, Oak Ridge
National Laboratory, for discussions which led to development of several com-
ponents of this system.
.
TA
...
.
...
REFERENCES
*c. F. Barnett, P. R. Bell, J. S. Luce, E. D. Shipley, and A. Simon,
Proc. U.N: Intern. Conf. Peaceful Uses Atomic Energy, 2nd, Geneva, 195
31, 298 (1959).
2. L. Dunlap, IRE Trans. Nucl. Sci. NS-7, No. 4, 19 (1960).
'H. Postma, IRE Trans. Nucl. Sci., NS-8, No. 4, 77 (1961).
*C. F. Barnett, J. L. Dunlap, R. S. Edwards, G. R. Haste, J. A. Ray,
R. G. Reinhardt, W. J. Schill, R. M. Warner, and E. R. Wells,
Nuclear Fusion 1, 264 (1961).
'J. L. Dunlap, C. F. Barnett, R. A. Dandi, and H. Postma, Nuclear Fusion:
1962 Supplement, Pt. 1, 233 (1962).
OJ. L. Dunlap, G. R. Haste, H. Postma, and L. H. Reber, Phys. Rev. Letters
14, 937 (1965).
'J. L. Dunlap, G. R. Haste, C. E. Nielsen, H. Postma, and L. H. Reber,
Phys. Fluids 9, 199 (1966).
°Manufactured by Telco, Inc., 575 Technology Square, Cambridge, Mass.
J. L. Dunlap, R. S. Edwards, G. R. Haste, L. A. Massengill, C. E. Nielsen,
H. Postma, R. G. Reinhardt, W. J. Schill, E. R. Wells, and R. A. Young,
Thermonuclear Div. Semiann. Progress Rept, Oct. 31, 1965, ORNL-3908, p. 2.
"H. Postma, J. L. Dunlap, R. A. Dory, G. R. Haste, and R. A. Young,
Phys. Rev. Letters 16, 265 (1966).
L. G. Kuo-Petravic', E. G. Murphy, M. Petravicí, R. M. Sinclair,
D. R. Sweetman, and E. Thompson, Culham Laboratory Rept. CLM-P 108 (1966).
15.
2
N.EMME
. 1.
10
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