The Physics of Inertial Fusion Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter

by Atzeni, Stefano; Meyer-ter-Vehn, Jürgen

• ISBN13: 9780198562641
• ISBN10: 0198562640
• Format: Hardcover
• Copyright: 2004-08-12
• Publisher: Clarendon Press

Summary

This book is on inertial confinement fusion, an alternative way to produce electrical power from hydrogen fuel by using powerful lasers or particle beams. Two huge laser facilities are presently under construction to show that this method works. It involves the compression of tiny amounts(micrograms) of fuel to thousand times solid density and pressures otherwise existing only in the centre of stars. Thanks to advances in laser technology, it is now possible to produce such extreme states of matter in the laboratory. Recent developments have boosted laser intensities again with newpossibilities for laser particle accelerators, laser nuclear physics, and fast ignition of fusion targets. This is a reference book for those working on beam plasma physics, be it in the context of fundamental research or applications to fusion energy or novel ultra-bright laser sources. The bookcombines quite different areas of physics: beam target interaction, dense plasmas, hydrodynamic implosion and instabilities, radiative energy transfer as well as fusion reactions. Particular attention is given to simple and useful modelling, including dimensional analysis and similarity solutions.Both authors have worked in this field for more than 20 years. They want to address in particular those teaching this topic to students and all those interested in understanding the technical basis.

Author Biography

Stefano Atzeni is Professor of Physics in the Dipartimento di Energetica, Universita di Roma "La Sapienza" and INFM, Italy. Jurgen Meyer-ter-Vehn is Professor of Physics at the Max Planck Institute for Quantum Optics, Garching, and at the Technical University of Munich, Germany.

Table of Contents

Nuclear fusion reactions	1	(30)
Exothermic nuclear reactions: fission and fusion	2	(1)
Fusion reaction physics	3	(7)
Cross section, reactivity, and reaction rate	3	(2)
Fusion cross section parametrization	5	(2)
Penetration factors for non-resonant reactions	7	(3)
Some important fusion reactions	10	(4)
Main controlled fusion fuels	12	(1)
Advanced fusion fuels	13	(1)
p--p cycle	14	(1)
CNO cycle	14	(1)
CC reactions	14	(1)
Maxwell-averaged fusion reactivities	14	(7)
Gamow form for non-resonant reactions	15	(2)
Reactivity of resonant reactions	17	(1)
Reactivities for controlled fusion fuels	18	(3)
Fusion reactivity in very high density matter	21	(3)
Electron screened, weakly coupled plasmas	22	(1)
Strongly coupled plasma	23	(1)
Crystalline solids: pycnonuclear limit	23	(1)
Spin polarization of reacting nuclei	24	(1)
μ-catalysed fusion	25	(2)
Historical note	27	(4)
Thermonuclear fusion and confinement	31	(16)
Thermonuclear fusion	32	(2)
Beam fusion versus thermonuclear fusion	32	(1)
Ideal ignition temperature	32	(2)
Plasma confinement	34	(1)
Magnetic confinement	34	(1)
Inertial confinement	34	(1)
Thermonuclear ignition: MCF versus ICF	35	(1)
Lawson-type and nτT ignition conditions for MCF	36	(2)
Power balance and energy confinement time	36	(1)
Lawson-type criterion	36	(1)
nτT ignition condition	37	(1)
Conditions for ignition and high gain in ICF	38	(3)
Confinement parameter ρR	38	(2)
Burn efficiency	40	(1)
The burn parameter HB	41	(1)
General requirements for IFE energy production	41	(3)
Gain required for IFE reactor	41	(1)
Admitted fuel mass	42	(1)
High fuel compression	43	(1)
Hot spot ignition and propagating burn	43	(1)
Fuel cycles	44	(3)
DT cycle and tritium breeding	44	(1)
Deuterium and advanced fuels	45	(2)
Inertial confinement by spherical implosion	47	(28)
Simulation of a spherical implosion	48	(17)
Target and laser pulse	49	(1)
The implosion diagram	50	(1)
Hollow shell targets driven by shaped pulses	51	(3)
Irradiation and implosion	54	(3)
Implosion stagnation and hot spot generation	57	(4)
Fuel ignition and burn	61	(2)
Summary of simulation results	63	(2)
Optimizing target gain	65	(1)
Symmetry and stability	65	(4)
Long-wavelength perturbations	66	(3)
Rayleigh--Taylor instabilities	69	(1)
Fusion target energy output	69	(1)
Historical note	70	(2)
Bibliographical note	72	(3)
Ignition and burn	75	(26)
Power balance of an igniting sphere	76	(5)
Fusion power deposition	77	(1)
Charged fusion products	77	(1)
Neutrons	78	(1)
Thermal conduction	79	(1)
Bremsstrahlung	79	(1)
Mechanical work	80	(1)
Central ignition of pre-assembled fuel	81	(6)
Self-heating condition	81	(1)
Ignition condition	82	(3)
Self-heating time	85	(2)
Dynamics of hot spot generation	87	(2)
Hot spot evolution and burn propagation	89	(4)
Early evolution and analytical ignition criterion	89	(3)
Self-regulating burn waves	92	(1)
Regimes of thermonuclear burn propagation	92	(1)
Volume ignition of optically thick fuel	93	(3)
Full burn simulations and burn efficiency	96	(1)
Ignition of pure deuterium	97	(1)
In summary	98	(3)
Energy gain	101	(28)
Hot spot ignition model	102	(4)
Target gain, fuel gain, coupling efficiency η	102	(1)
Hot spot	103	(1)
Cold fuel: isentrope parameter α	104	(1)
Isobaric configuration: pressure p	105	(1)
Gain curves of the isobaric model	106	(4)
Dependence on η, α, and p	107	(2)
Model gain curves versus detailed computations	109	(1)
Limiting gain curves	110	(7)
Gain curve for a given fuel mass	110	(1)
Analytic derivation of the limiting gain	111	(3)
Minimum energy to burn a given fuel mass	114	(2)
Shortcomings and extensions of the model	116	(1)
Constrained gain curves and target design	117	(6)
Ablation pressure and velocity of the imploding shell	119	(1)
Scaling of ignition energy with implosion velocity	119	(2)
Laser power---laser energy window	121	(2)
Gain curves for non-isobaric configurations	123	(6)
Isochoric assemblies with hot spot	123	(1)
Volume-ignited optically thick DT fuel	124	(2)
Comparing different configurations and fuels	126	(3)
Hydrodynamics	129	(66)
Ideal gas dynamics	130	(4)
Basic equations in conservative form	130	(1)
Physical limitations	130	(1)
Euler representation	131	(1)
One-dimensional Lagrange representation	132	(2)
Shocks	134	(4)
Discontinuities	134	(1)
Hugoniot condition	135	(1)
Shock in ideal gas	136	(1)
Weak shocks	136	(1)
Strong shocks	137	(1)
Rarefaction shocks and shock stability	137	(1)
Plane isentropic flow	138	(10)
Isentropic flow	139	(1)
Characteristics and Riemann invariants	139	(2)
Simple waves	141	(2)
Centred rarefaction	143	(1)
Isentropic compression to arbitrary density	144	(2)
Rarefaction in Lagrange coordinates	146	(1)
Isothermal rarefaction wave	147	(1)
Radial flows with u(r,t) α r	148	(9)
Homogeneous adiabatic flow	149	(1)
Kidder's cumulative implosion	150	(2)
Stagnating flow	152	(5)
Dimensional analysis	157	(4)
Π-Theorem	158	(1)
Example: point explosion	159	(2)
Symmetry groups and similarity solutions	161	(9)
Some elements of Lie group theory of DE	161	(2)
Lie group of ID hydrodynamics	163	(1)
Classes of invariant solutions	164	(3)
Scale-invariant solutions	167	(1)
Solutions exponential in time	167	(1)
S3 and S4 symmetry	168	(1)
New solutions by projection	168	(2)
Scale-invariant similarity solutions	170	(25)
Similarity coordinates	171	(1)
Particle trajectories and characteristics	172	(1)
Conservation of mass and entropy	173	(1)
Reduction to ODE	174	(2)
Synopsis of solutions in the U, C plane	176	(1)
Singular points	177	(4)
Shock boundaries	181	(1)
Central explosions (P6 flow)	182	(3)
Cumulative implosions (P5 flow)	185	(2)
Uniform gas compression	187	(1)
Guderley's imploding shock wave	188	(2)
Imploding non-isentropic shells	190	(1)
Stagnation pressure of imploding shells	191	(1)
Implications for ICF target implosions	192	(3)
Thermal waves and ablative drive	195	(42)
Transport by electrons and photons	196	(2)
General discussion	196	(1)
Diffusion and heat conduction	196	(2)
Electron heat conduction	198	(3)
Fokker--Planck treatment	198	(1)
Steep temperature gradients and flux limitation	199	(2)
Radiative transport	201	(4)
Spectral intensity and transfer equation	201	(1)
Local thermal equilibrium and Kirchhoff's law	202	(1)
Diffusion approximation	203	(1)
Two-temperature grey approximation	204	(1)
Radiative heat conduction	204	(1)
Non-stationary thermal waves	205	(4)
Different types of thermal waves	205	(1)
Self-similar thermal waves: dimensional analysis	206	(3)
Self-regulating heating wave	209	(4)
The supersonic heating wave	209	(1)
The ablative heating wave	210	(1)
Application to laser-driven ablation	210	(3)
Ablative heat wave	213	(3)
The general solution	213	(1)
Application to high-Z wall	214	(2)
Stationary ablation	216	(8)
Deflagration and detonation	217	(2)
X-ray driven ablation	219	(2)
X-ray ablation pressure and mass ablation rate	221	(2)
Supersonic X-ray heating	223	(1)
Stationary laser-driven ablation	224	(3)
The role of the critical density	224	(1)
Scaling of laser-driven stationary ablation	225	(1)
The conduction layer	226	(1)
Stationary ablation fronts in accelerated frame	227	(3)
Solutions for plane geometry	227	(2)
Numerical results	229	(1)
Spherical rocket drive	230	(7)
The rocket equations	231	(1)
Spherical implosion parameter	231	(1)
Implosion velocity and hydrodynamic efficiency	232	(2)
Implosion velocity and in-flight aspect ratio	234	(3)
Hydrodynamic stability	237	(64)
Fluid instabilities and ICF: a preview	238	(5)
Rayleigh--Taylor instability	238	(3)
RTI and ICF	241	(1)
Richtmyer--Meshkov instability	242	(1)
Kelvin-Helmoltz instability	243	(1)
Stability of plane interfaces	243	(14)
Potential flow equations for incompressible fluids	243	(2)
Fluid boundaries	245	(1)
Small perturbations: linearized equations	246	(1)
Normal mode analysis and dispersion relation	247	(2)
Classical RTI growth rate	249	(1)
Influence of viscosity and compressibility on RTI	250	(1)
KHI growth rate	251	(1)
Time evolution	252	(1)
RTI of layers of finite thickness and feedthrough	253	(2)
RMI growth rate	255	(1)
Non-uniform acceleration	256	(1)
RTI in fluids with arbitrary density profile	257	(4)
Linearized perturbation equations	257	(2)
General instability condition	259	(1)
The classical RTI growth rate	259	(1)
Density gradient	260	(1)
RTI at an ablation front	261	(13)
Isobaric flow model	262	(2)
Discussion in terms of the Froude number and of the conductivity exponent v	264	(2)
Perturbation equations	266	(2)
Results of self-consistent treatments	268	(3)
Comparison with experiments and simulations	271	(3)
Stability of spherical boundaries	274	(5)
Perturbation equation for a cavity	275	(1)
Stability of a spherical cavity. Cavity oscillations	275	(2)
Classical RTI at implosion stagnation	277	(1)
Ablative RTI of decelerating ICF shells	278	(1)
Non-linear evolution of single-mode perturbations	279	(7)
RTI bubble evolution for At = 1	280	(3)
Asymptotic bubble and spike behaviour for arbitrary At	283	(1)
Linear saturation amplitude of a single RTI mode	284	(1)
3D versus 2D non-linear RTI evolution	285	(1)
Non-linear evolution of multi-mode perturbations	286	(5)
Preview and relevance to ICF targets design	286	(1)
Growth saturation of a full spectrum of modes	287	(2)
Model for weakly non-linear evolution after saturation	289	(1)
Turbulent mixing	290	(1)
RTI and target design	291	(7)
Perturbation growth at the ablation front	292	(2)
Perturbation growth at the inner shell surface	294	(1)
Target stability analysis by models and fluid codes	295	(2)
Reducing target sensitivity to RTI	297	(1)
Bibliographical note	298	(3)
Hohlraum targets	301	(22)
General concept	302	(2)
Conversion into X-rays	304	(4)
Laser beam conversion	304	(2)
Ion beam conversion	306	(2)
Radiation confinement	308	(4)
Hohlraum temperature	308	(1)
Flux balance	309	(1)
Wall albedo and re-emission number	310	(1)
Re-emission experiments and observed hohlraum temperatures	311	(1)
Geometrical symmetrization	312	(3)
Spherical asymmetry modes	312	(1)
View factor method	313	(1)
Transfer between concentric spheres	314	(1)
Hohlraum target simulations	315	(5)
A hohlraum target for heavy ion fusion	315	(3)
Radiatively driven capsule with optimized opacity	318	(2)
Hohlraum target experiments	320	(3)
Experiments on hohlraum symmetry	321	(1)
Shock wave experiments with hohlraum targets	321	(2)
Hot dense matter	323	(48)
Atoms in dense plasma	324	(4)
The screened hydrogenic model	324	(2)
The average ion model	326	(1)
Pressure ionization	326	(1)
Continuum lowering	327	(1)
Ideal dense plasma	328	(4)
Thermodynamic relations	328	(1)
Ideal gas and Saha ionization	329	(1)
Fermi gas	330	(2)
Thomas-Fermi theory	332	(4)
Basic TF equations	332	(1)
TF electron equation of state	333	(2)
Explicit formula for TF pressure-ionization	335	(1)
Total binding energy of neutral atoms in the TF statistical model	336	(1)
Ion EOS model	336	(3)
Phonon EOS of solids	337	(1)
Cowan's model for a fluid EOS	338	(1)
Global equations of state	339	(6)
General discussion	339	(3)
QEOS: A general purpose equation of state	342	(1)
Correction for chemical bonding	343	(1)
QEOS examples	343	(2)
Radiative processes	345	(11)
Micro-reversability and detailed balance	345	(2)
Quasi-classical derivation of Kramers cross section	347	(1)
Bremsstrahlung emission and absorption	348	(1)
Radiative capture and photo-ionization	349	(1)
Line emission and absorption	350	(2)
Doppler and Stark broadening	352	(2)
Sum rule and spectral spreading of oscillator strength	354	(1)
Unresolved transition arrays and super-transition arrays	355	(1)
Opacity	356	(7)
Planck and Rosseland mean opacity	356	(1)
Explicit formulas for fully ionized plasma	356	(1)
Photon scattering	357	(1)
Maximum opacity limit	357	(1)
Opacity calculations	358	(1)
Results of simple LTE opacity models	358	(3)
Opacity experiments	361	(2)
Non-LTE plasma	363	(2)
Non-LTE ionization	363	(1)
Non-LTE opacity	364	(1)
Electron collisions	365	(6)
Collision times in dilute plasma	365	(2)
Collision frequency in warm dense matter for T ≤ TF	367	(1)
Collisional ionization of inner-shell electrons	368	(1)
Collisional ionization rate in plasma	369	(1)
Three-body recombination	370	(1)
Beam-target interaction	371	(38)
Elements of plasma physics	372	(5)
Transverse electromagnetic waves	373	(1)
Longitudinal dispersion	374	(2)
Langmuir waves	376	(1)
Ion-acoustic waves	377	(1)
Collisional absorption of laser light in plasma	377	(4)
Absorption coefficient	378	(1)
Model for collisional absorption	379	(1)
Dependence on wavelength	380	(1)
Resonance absorption	381	(2)
Coupling of light and plasma waves in density gradients	381	(1)
Theoretical absorption curve	382	(1)
Comparison with experiment	382	(1)
Light absorption and scattering by wave excitation	383	(6)
The ponderomotive force	383	(2)
Three-wave coupling and parametric instabilities	385	(1)
Parametric decay	386	(1)
Two-plasmon decay	386	(1)
Stimulated Brillouin scattering	387	(1)
Stimulated Raman scattering	388	(1)
Hot electrons	388	(1)
Theory of ion beam energy loss in plasma	389	(10)
Stopping fast ions by binary collisions	389	(2)
Projectile wakefield in the dielectric approach	391	(1)
Stopping power in plasma	392	(1)
Excitation of plasma waves by fast ions (υp/υth << 1)	393	(1)
The Bethe formula	394	(1)
Stopping power for slow ions (υp ≤ υth)	394	(1)
Non-linear friction force	395	(1)
Approximate plasma stopping formula for arbitrary υp	396	(1)
Stopping of charged fusion products in burning plasma	396	(3)
The effective charge Zeff of heavy ions	399	(5)
Semi-empirical description of Zeff(υ)	399	(1)
Ionization and recombination processes	400	(1)
Measurements of Zeff behind target	401	(2)
Projectile radiation measured in flight	403	(1)
Ion stopping powers and ranges in cold and hot matter	404	(5)
Stopping in partially ionized matter	404	(1)
Ion ranges in cold matter	405	(1)
Enhanced dε / dx in plasma	405	(1)
Examples of dε / dx and R in dense plasma	406	(3)
Fast ignition	409	(20)
Concepts and perspectives	410	(1)
Ignition conditions and fuel energy gain	411	(2)
The one-dimensional isochoric model	411	(1)
Ignition windows	412	(1)
Admitted beam particle ranges	413	(1)
Fuel gain of fast ignition targets	413	(1)
New perspectives by fast ignition	413	(3)
Injected triggers	413	(1)
Non-spherical configurations	414	(1)
Burn of a DT-seeded deuterium target	415	(1)
Laser plasma physics at relativistic intensities	416	(5)
Laser fast ignition	416	(1)
Relativistic laser plasma interaction	417	(1)
Self-focusing and electron beam generation	418	(1)
Channels and beams observed	419	(1)
Mechanisms of electron acceleration	420	(1)
Electron beam transport through overdense plasma	421	(4)
Laser hole boring	422	(1)
Alfven current limit and Weibel instability	423	(1)
Beam filamention and anomalous stopping	424	(1)
Electron transport experiments	425	(1)
Emerging fast ignition concepts	425	(4)
Cone-guided fast ignition	425	(1)
Cone-guided target experiments	426	(1)
Proton beam fast ignition	427	(2)
Appendix	429	(6)
A. Units and conversion of units	429	(1)
B. Physical constants	430	(1)
C. Frequently used symbols	431	(2)
D. Acronyms	433	(2)
References	435	(18)
Index	453