Download Introduction Multi-Pass Stochastic Heating Particle-in

Computational Simulations of
Multi-Pass Stochastic Heating
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Xin Zhang
Tom Donnelly
Todd Ditmire
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Harvey Mudd College
University of Texas at Austin
Introduction
M
ulti-pass stochastic heating is
a proposed mechanism through
which laser energy is coupled into solid target. Theoretically, stochastic heating should be highly efficient when a
high-intensity laser pulse irradiates a
wavelength-scale target. In this study,
we try to understand the basic physics of
stochastic heating, and build a numerical
model to simulate the process.
Multi-Pass Stochastic Heating
D
uring the heating process, electrons in the plasma will absorb
energy from the strong-field laser and
eventually escape the plasma. This leaves
positively charged ions in the plasma
closely packed, resulting in a system with
high potential energy. The plasma subsequently expands, converting potential
energy to the kinetic energy of the ions
(Fig.1).
W
hen an free
electron
is exposed to the
oscillating electric field of the Figure 1. Schematic of Multilaser pulse, the pass stochatic heating.
electron accelerates coherently with the electric field.
When the pulse leaves, the electron will
also stop oscillating. Under this condition, the electron has a non-zero time
average kinetic energy during the pulse,
but has no net energy gain from the laser
field after the pulse leaves (Fig. 2).
W
hen the driven electron is inside a plasma, the situation changes. The electron
will first be accelerated by the laser field as before. After it enters the boundary of plasma,
the external electric field is shielded, the electron move with constant velocity, and therefore
loses coherence with the laser field. After it resurfaces from the other side of the plasma and
enters free space again, it receives another kick
from the electric field, accelerates, and the process repeats (Fig. 1). In this regime, the electron has a non-zero velocity left over (Fig. 2).
Figure 2. Electron acceleration by laser field, with
(blue) and without plasma shielding (orange).
The laser is modeled as a
sine wave with a Gaussian
wave packet. The velocity
of the electron (above) is
found by integrating the
external field (below) (arbitrary units). The electron gained a significant
amount of kinetic energy
when shielding is present
(flat regions).
Particle-in-Cell Simulations
P
P
article-in-Cell (PIC) algorithms are the most popular method for simulating the
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behavior of plasmas. For physically meaningful plasma, we can easily have 10 particles to keep track of, which is very computationally expensive.
IC codes are a class of algorithms
Input/Output
that reduce the computational complexity of many particle systems. In a
Calculating
charge
Solving
Maxwell’s
PIC code, physical particles in a system
and
current
density
equations
are represented by a collection of computational particles, each of which repIntegrating
particle
Finding
forces
on
resents a large collection of physical parequations of motion
each particle
ticles - so-called “super-particles”. The
workflow of PIC algorithms is shown in Figure 3. Flow chart of Particle-in-Cell Algorithms.
Fig.3
ll parts of the computational cycle of
a PIC program have been implemented with the aid of the dealII finite element
library; we solve the electrostatic Maxwell’s
equations under non-relativistic conditions.
Figure 4 shows a series of potentials that reFigure 4. Electrostatic
sult from imposing a constant external elecpotential obtained from
sample PIC simulation.
tric field to a square grid of particles. The
Particles are loaded into a
potential inside the grid is shown after the
square grid at random losystems reach equilibrium (time development
cations, with Maxwellian
velocity distributions.
not shown).
A
Future Work
W
ithin the PIC program, the next
steps will be to implement the
electro-dynamics solution, add the ion
background, and then finally consider
non-zero magnetic fields. It is also possible to parallelize the program to get better computational performance.
hen the PIC program is complete, we will be able to perform
a numerical simulation of multi-pass
stochastic heating. In the longterm, we
hope to produce data sets that can be
compared with our experimental results.
e are also currently implementing
an idealized model of stochastic
heating in Mathematica to try to understand what parameters (e.g. intensity
of laser, dimensions of the plasma, etc.)
influence the electron energy spectrum
and how. Upon completion, it should
provide insights into the basic physics of
stochastic heating.
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Acknowledgements
I
would like to thank my advisor, Prof.
Donnelly, without whom none of this
could have been possible; my modeling buddy Casey Cannon for keeping me
company in those long hours of debugging; Jim Wu for letting me talk at him
and providing a fresh perspective; and the
rest of our group: Amber
Cai, Sophie Blee-Goldman, Caleb Eades, and
Hao Cao for all their support and a wonderful research experience.
Copyright © 2016 Xin Zhang