EM-PIC simulations of e-beam interaction with field emitted ions from bremsstrahlung targets Page: 4 of 6
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pulse time of 60 ns. Of course this theory is quite
simplified; we next turn to self consistent simulations.
3. EM-PIC SIMULATIONS
Direct particle-in-cell (PIC) simulation of intense
beams has a long and successful history, both at LLNL
and elsewhere. We have simulated ion emission and
subsequent beam defocusing with both CONDOR, a w
tested design code developed over many years within A
division, and a new code, CODA, that allows non-
rectangular zones. Both codes are fully relativistic, 2-1
dimensional (2-spatial dimensions in axisymmetric Z-
geometry, 3-velocity dimensions) electromagnetic (EM
PIC codes. The simulation geometry is a cylinder of
radius 4 cm and length 25 cm with conducting bounder
The beam is injected at the left hand boundary with an
initial radius of 2.0 cm, and with uniform current dens
The beam is injected with finite emittance so as to be
focused at the target; no externally applied fields are
present. The injected beam current is linearly ramped u
10 ns, constant for 40 ns, then linearly ramped down
again in 10 ns. The right hand end-plate forms the
absorbing target, from which ions are emitted. No
modeling of the target heating or surface physics is
included; the space-charge-limited emission is simply
turned on at a preselected time, over a specified radial
region. Simulations presented here were all performed
with CODA utilizing a converging mesh that allows
much better resolution at the target surface, Ar=200
and Az=600 pm.
The time history of the RMS beam radius at the
target is shown in Fig. 1 from a typical simulation. T
injected beam is characteristic of FXR, with Ib=2.3 k
Eb=16 MeV (yb-32) and initially focused to a root-me
squared (RMS) radius rb=0.06 cm. Proton emission is
turned on at t=15 ns, in the region 0<r<0.06 cm. The
initial pinch and subsequent defocus occur very quickly0.3
0.2
0.1
0.00
20
40
t (ns)
Fig. 1 Time dependent beam radius at target from a
simulation of FXR with proton emission turned on at
t=15ns.ell-
/2
R
)e
ies.agreement with our previous estimate. As the beam
defocuses, emission decreases (from a peak of I;=8 A)
because of the reduced electric field at the emission area.
Many aspects of the simple theory previously developed
are observed in these simulations, namely the magnitude
of the axial electric field at the target surface, the time for
pinching to occur, and the small ratio of emitted ion
current to beam current (<1%). The scaling of the time to
defocus, Eq. (3), with ion mass and beam current has also
been confirmed by additional simulations. An important
observation is that the total number of field emitted ions,
Ni, is quite small: for this simulation Ni=5.7x10" at
t=30 ns. This corresponds to a fraction of approximately
104 from a monolayer of equal area, suggesting that
surface cleaning would be a very difficult proposition.ity. 4. COMPARISON WITH FXR DATA
We now consider available data from FXR. Two
principle measurements are used to assess spot quality at
p in FXR; both are time-integrated radiographic measurements.
The first uses an opaque "roll bar" to cast a shadow from
the bremsstrahlung spot; the width of the edge of this
shadow reflects the finite spot size. Careful unfolding of
the data shows a central peak with FWHM spot size of
1.1mm, surrounded by a low density "halo" with relative
brightness of a few percent of the central peak [2]. In the
second measurement, forward bremsstrahlung dose is
measured both with and without an 800 pm diameter
m collimator. The collimated dose is observed to be
approximately 1/3 of the forward dose in the absence of
the collimator; this is observed to be the case both for
he beam currents of 2.3 kA and 3.3 kA [3].
, Although the experimentally observed small spot
an seems at odds with the defocusing seen in the simulations,
e.g. Fig. 1, this is not necessarily so. Because the beam
density at the target is inversely proportional to the square
in of the spot size, nbcI/r2, the bremsstrahlung emission
from the defocused beam is very dim and a time integrated
measurement can be dominated by the early-time small
spot brightness. In Figure 2, we show the time integrated
beam density at the target (normalized) as a function of
radius from the simulation illustrated in Fig. 1. As can be
seen, the contribution from the defocused beam is a low
density halo. The level of the halo relative to the central
peak is determined by the relative duration of the focused
and unfocused periods of the time history. This is
illustrated in Fig. 2, which also shows results from
simulations with the ion emission turned on at 10 and
30 ns. The level of the halo is also affected by the
defocused radius; allowing ion emission from a larger area
increases the defocused beam spot, decreasing the relative
beam density in the halo.
We next consider the collimated dose measurements.
The angular spectrum of bremsstrahlung photons created
by 16 MeV electrons striking a 1mm thick Ta target was
calculated using a Monte Carlo code [4]; this angular
spectrum is then used to determine the contribution to the
forward dose from each simulation electron as it strikes
the target. Figure 3 shows the time dependent forward
dose (normalized) for the simulation shown in Fig. 1.
Because the electrons strike the target with larger angles- H---i 'i''' . . H 1 U I 1 U I ...-
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Rambo, P. W., LLNL. EM-PIC simulations of e-beam interaction with field emitted ions from bremsstrahlung targets, article, August 13, 1998; California. (https://digital.library.unt.edu/ark:/67531/metadc683360/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.