D
~ffu~a-
f~a~~olm
BEAM
PLASMA
INTERACTION,
HYDRODYNAMICS,
HOT
DENSE
MATTER
STEFANO
ATZENI
Universitä
di
Roma
`La
Sapienza'
and
INFM
Italy
TÜRGEN
MEYER-TER-VEHN
Max-Planck-Institut
für
Quantenoptik,
Garching,
Germany
CLARENDON
PRESS
-OXFORD
2004
Contents
Nuclear
fusion reactions
1
1
.7
1%-catalysed fusion
25
1
.1
Exothermic
nuclear
reactions
:
fission
1 .8
Historical
note
27
and
fusion
2
1 .2
Fusion
reaction
physics
3
2
Thermonuclear
fusion
and
1
.2 .1
Cross
section,
reactivity,
confinement
31
and
reaction
rate
3
1
.2
.2
Fusion
cross
section
2
.1
Thermonuclear
fusion
32
parametrization
5
2
.1 .1
Beam
fusion versus
1
.2
.3
Penetration
factors
for
thermonuclear
fusion
32
non-resonant
2
.1
.2
Ideal
ignition
reactions
7
temperature
32
1 .3
Some
important
fusion
2
.2
Plasma
confinement
34
reactions
10
2
.2
.1
Magnetic
confinement
34
1 .3 .1
Main
controlled
fusion
2
.2 .2
Inertial
confinement
34
fuels
12
2
.3
Thermonuclear
ignition
:
MCF
versus
1
.3 .2
Advanced
fusion
fuels
13
ICF 35
1
.3
.3
p-p
cycle
14
2
.4
Lawson-type
and
nrT
ignition
1
.3
.4
CNO
cycle
14
conditions
for
MCF
36
1
.3
.5
CC
reactions
14
2
.4
.1
Power
balance
and energy
1
.4
Maxwell-averaged
fusion
confinement
time
36
reactivities
14
2
.4
.2
Lawson-type
criterion
36
1
.4
.1
Gamow
form
for
2
.4
.3
nrT
ignition
non-resonant
reactions
15
condition
37
1
.4 .2
Reactivity
of
resonant
2
.5
Conditions
for
ignition
and
high
gain
reactions
17
in
ICF
38
1
.4
.3
Reactivities
for
controlled
2
.5 .1
Confinement
parameter
p12
38
fusion
fuels
18
2
.5 .2
Burn
efficiency
40
1
.5
Fusion
reactivity
in
very high
density
2
.5
.3
The
burn
parameter
Hp
41
matter
21
2
.6
General
requirements
for
IFE
energy
1 .5 .1
Electron
screened,
weakly
production
41
coupled
plasmas
22
2
.6
.1
Gain
required
for
IFE
1
.5
.2
Strongly
coupled
plasma
23
reactor
41
1
.5 .3
Crystalline
solids
:
2
.6 .2
Admitted
fuel
mass 42
pycnomaclear
limit
23
2
.6 .3
High
fuel
compression
43
1
.6
Spin
polarization
of
reacting
2
.6 .4
Hot
spot
ignition
and
nuclei
24
propagating
burn
43
xvi
Contents
2
.7
Fuel
cycles
44
4
.2 .2
Ignition
condition
82
2
.7
.1
DT
cycle
and
tritium
4
.2 .3
Self-heating
time
85
breeding
44
4
.3
Dynamics
of
hot
spot
2
.7 .2
Deuterium
and
advanced
generation
87
fuels
45
4
.4
Hot
spot
evolution
and
burn
propagation
89
4
.4
.1
Early
evolution
and
analytical
ignition
3
Inertial
confinementby
spherical
criterion
89
implosion
47
4
.4 .2
Self-regulating
bum
3
.1
Simulation
of
a spherical
waves
92
implosion
48
4
.4 .3
Regimes
of
thermonuclear
3
.1
.1
Target
and
laser
pulse
49
burn
propagation
92
3
.1
.2
The
implosion
diagram
50
4
.5
Volume
ignition
of
optically
thick
3
.1
.3
Hollow
shell
targets
driven
fuel
93
by
shaped
pulses
51
4
.6
Full
burn simulations
and
burn
3
.1
.4
Irradiation
and
implosion
54
efficiency
96
3
.1
.5
Implosion
stagnation
and
4
.7
Ignition
of pure
deuterium
97
hot
spot
generation
57
4
.8
In
summary
98
3
.1
.6
Fuel
ignition
and
burn 61
3
.1
.7
Summary
of
simulation
results
63
3
.1 .8
Optimizing
target
gain
65
5
Energy
gain
101
3
.2
Symmetry
and
stability
65
3
.2
.1
Long-wavelength
5
.1
Hot
spot
ignition
model
102
perturbations
66
5
.1
.1
Target
gain,
fuel
gain,
3
.2
.2
Rayleigh-Taylor
coupling
efficiency
n
102
instabilities
69
5
.1
.2
Hot
spot
103
3
.3
Fusion
target
energy
output
69
5
.1
.3
Cold
fuel
;
isentrope
3 .4
Historical
note
70
parameter
a
104
3,5
Bibliographical
note
72
5
.1
.4
Isobaric
configuration
:
,
pressure
P
105
5
.2
Gain
curves
of
the isobaric
model
106
5
.2
.1
Dependence
on
n,
a,
Ignition
and
burn
75
and
p
107
5
.2 .2
Model
gain
curves versus
4
.1
Power
balance
of an
igniting
detailed
computations
109
sphere
76
5
.3
Limiting
gain
curves
110
4
.1
.1
Fusion
power
deposition
77
5
.3 .1
Gain
curve
for a
given
4
.1 .2
Charged
fusion
products
77
fuel
mass 110
4
.1 .3
Neutrons
78
5
.3 .2
Analytic
derivation
of
the
4
.1
.4
Thermal
conduction
79
limiting
gain
]I]
4
.1
.5
Bremsstrahlung
79
5
.3
.3
Minimum
energy
to
burn
a
4
.1
.6
Mechanical
work
80
given
fuel
mass
114
4
.2
Central
ignition
of
pre-assembled
5
.3 .4
Shortcomings
and
fuel
81
extensions
of
the
4
.2
.1
Self-heating
condition
81
model
116
Contents
xvii
5
.4
Constrained
gain
curves
and
target
6
.3
.7
isothermal
rarefaction
design
117
wave
147
5
.4 .1
Ablation
pressure
and
6
.4
Radial
flows
with
u(r,t)
oc
r
148
velocity
of
the
imploding
6
.4
.1
Homogeneous
adiabatic
shell
119
flow
149
5
.4
.2
Scaling
of
ignition
energy
6
.4 .2
Kidder's
cumulative
with
implosion
velocity
119
implosion
150
5
.4
.3
Laser
power-laser
energy
6
.4,3
Stagnating
flow
152
window
121
6
.5
Dimensional
analysis
157
5
.5
Gain
curves
for
non-isobaric
6
.5 .1
Il-Thcorem
158
configurations
123
6
.5 .2
Example
:
point
5
.5
.1
Isochoric
assemblies
with
explosion 159
hot
spot
123
6
.6
Symmetry
groups
and
similarity
5
.5 .2
Volume-ignited
optically
solutions
161
thick
DT
fuel
124
6
.6
.1
Some
elements
of
Lie
group
5
.5
.3
Comparing
different
theory
of
DE
161
configurations
and
fuels
126
6
.6
.2
Lie
group
of
1D
hydrodynamics
163
6
.6,3
Classes
of
invariant
solutions
164
6
Hydrodynamics
129
6
.6
.4
Scale-invariant
solutions
167
6
.6
.5
Solutions
exponential
in
6
.1
Ideal
gas
dynamics
130
time
167
6
.1
.1
Basic
equations
in
6
.6 .6
S3
and
S4
symmetry
168
conservative
form
130
6
.6
.7
New
solutions
by
6
.1
.2
Physical
limitations
130
projection
168
6
.1
.3
Euler
representation
131
6
.7
Scale-invariant
similarity
6
.1
.4
One-dimensional
Lagrange
solutions
170
representation
132
6
.7
.1
Similarity
coordinates
171
6
.2
Shocks
134
6
.7
.2
Particle trajectories
and
6
.2 .1
Discontinuities
134
characteristics
172
6
.2 .2
Hugoniot
condition
135
6
.7 .3
Conservation of
mass
and
6
.2
.3
Shock
in ideal
gas
136
entropy
173
6
.2 .4
Weak
shocks 136
6
.7
.4
Reduction
to
ODE
174
6
.2
.5
Strong
shocks
137
6
.7
.5
Synopsis of
solutions
in
the
6
.2 .6
Rarefaction
shocks
and
U,
C
plane
176
shock
stability
137
6
.7 .6
Singular
points
177
6
.3
Plane
isentropic
flow
138
6
.7 .7
Shock
boundaries
181
6
.3
.1
Isentropic
flow
139
6
.7 .8
Centrat
explosions
6
.3 .2
Characteristics
and
(Pr,
flow)
182
Riemann
invariants
139
6
.7 .9
Cumulative
implosions
6
.3 .3
Simple waves
141
(PS
flow)
185
6
.3
.4
Centred
rarefaction
143
6
.7,10
Uniform
gas
compression
187
6
.3
.5
Isentropic
compression
to
6
.7
.11
Guderley's
imploding
shock
arbitrary
density
144
wave
188
6
.3
.6
Rarefaction
in
Lagrange
6,7 .12
Imploding
non-isentropic
coordinates
146
shells
190
Will
Contents
6
.7
.13
Stagnation
pressure
of 7
.7 .3
X-ray
ablation
pressure
and
imploding
shells
191
mass
ablation
rate
221
6
.7
.14
Implications
for
ICE
target
7
.7
.4
Supersonic
X-ray
implosions
192
heating
223
7
.8
Stationary
laser-driven
ablation
224
7
Thermal
waves
and
ablative
7
.8 .1
The
role
of
the
critical
drive
195
density
224
7
.8
.2
Scaling
of
laser-driven
7
.1
Transport
by
electrons
and
stationary
ablation
225
photons
196
7
.8
.3
The
conduction
layer
226
7
.1
.1
General
discussion
196
7,9
Stationary
ablation
fronts
in
7
.1
.2
Diffusion
and
heat
accelerated
frame
227
conduction
196
7
.9
.1
Solutions
for
plane
7
.2
Electron
heat
conduction
198
geometry
227
7
.2
.1
Fokker-Planck
treatment 199
7
.9 .2
Numerical
results
229
7
.2
.2
Steep
temperature
gradients
7,10
Spherical
rocket
drive
230
and
flux
limitation
199
7 .10
.1
The
rocket
equations 231
7
.3
Radiative
transport
201
7
.10
.2
Spherical
implosion
7
.3
.1
Spectral
intensity
and
parameter 231
transfer
equation
201
7 .10
.3
Implosion
velocity
and
7
.3 .2
Local
thermal
equilibrium
hydrodynamic
and
Kirchhoff's
law
202
efficiency
232
7
.3
.3
Diffusion
approximation
203
7
.10
.4
Implosion
velocity
and
7
.3
.4
Two-temperature
grey
in-flight
aspect
ratio
234
approximation
204
7
.3
.5
Radiative
heat
conduction
204
7
.4
Non-stationary
thermal
waves
205
8
Hydrodynamic
stability
237
7
.4
.1
Different
types
of
thermal
8,1
Fluid
instabilities
and
ICF
:
waves
205
a
preview
238
7
.4
.2
Self-similar
thermal
waves
:
8
.1 .1
Rayleigh-Taylor
dimensional
instability
238
analysis
206
8
.1
.2
RTI
and
ICF
241
7,5
Self-regulating
heating
wave 209
8
.1
.3
Richtmyer
Meshkov
7
.5
.1
The
supersonic
heating
instability
242
wave
209
8,1
.4
Kelvin-Helmoltz
7
.5
.2
The
ablative
heating
instability
243
wave
210
8,2
Stability
of
plane
interfaces
243
7
.5
.3
Application
to
laser-driven
8
.2
.1
Potential
flow
equations
for
ablation
210
incompressible
fluids
243
7
.6
Ablative
heat
wave
213
8
.2 .2
Fluid
boundaries
245
7
.6
.1
The
general
solution
213
8
.2
.3
Small
perturbations
:
7
.6 .2
Application
to
high-Z
linearized
equations
246
wall
214
8
.2
.4
Normal
mode
analysis
and
7
.7
Stationary
ablation
216
dispersion
relation
247
7
.7
.1
Deflagration
and
8
.2
.5
Classical
RTI
growth
rate
249
detonation
217
8
.2 .6
Influence
of
viscosity
and
7
.7 .2
X-ray
driven
ablation
219
compressibility
on
RTI
250