Experiments on Dynamic Overpressure Stabilization of the Ablative Richtmyer-Meshkov Instability ...

193 Pages·2004·2.13 MB·English

Experiments on Dynamic Overpressure Stabilization of the
Ablative Richtmyer-Meshkov Instability in ICF Targets
by
Orlin V. Gotchev
Submitted in Partial Ful(cid:28)llment
of the
Requirements for the Degree
Doctor of Philosophy
Supervised by
Professor David D. Meyerhofer
Department of Physics and Astronomy
The College
Arts and Sciences
University of Rochester
Rochester, New York
2004
ii
CURRICULUM VITAE
The author was born in Nedelino, Smolian region, Bulgaria on December 12,
1972. He attended the University of So(cid:28)a from September 1993 to June 1997,
working towards the degree of Magister in Physics. Based on his academic
record, intheSpringof1998hewasadmitedtotheUniversityofRochesteras
a graduate student in the Department of Physics and Astronomy. He began
graduate studies in the (cid:28)eld of High Energy Density Physics and Inertial
Con(cid:28)nement Fusion (ICF) at the Laboratory for Laser Energetics, under
Professor David D. Meyerhofer and Dr. James P. Knauer. In 1999-2004 he
was awarded a F. J. Horton Fellowship. He earned a Master of Arts degree
from the University of Rochester in 2000. The subject of his research are the
seeding mechanisms and stabilization of hydrodynamic instabilities before,
and during the acceleration phase of ICF implosions.
iii
ACKNOWLEDGMENTS
I would like to express my most sincere gratitude to my advisor Professor
David Meyerhofer for his insightful guidance, unobtrusive and to the point
advice, encouragement to work independently and for sharing his vast ex-
pertise as an experimentalist and physicist. This work would not have been
possible without him.
It is di(cid:30)cult to overstate my appreciation to Dr. James Knauer, my
LLE supervisor, who was so often my direct connection between a research
problem and the right path to its solution. I thank him for sharing his
thorough physical understanding, intuition and experience.
I’m extremely grateful to Dr. Valeri Goncharov, whose analytic mind
and physics understanding can be matched by few, and who never objected
sharing them with me. To him and his brilliant colleagues goes the credit for
the sound theoretical background that makes this thesis possible.
I am greatly indebted to Dr. Thomas Boehly, Dr. Paul Jaanimagi, Dr.
Frederic Marshall, and Dr. Vladimir Smalyuk, each of whom have con-
tributed in a special way to the research described in this thesis and to the
experience and knowledge I have gained in the process.
iv
I wish to express my great appreciation to my professors and LLE scien-
tists Riccardo Betti, Robert McCrory and Albert Simon, each of whom have
added in their unique way to my never su(cid:30)cient scienti(cid:28)c knowledge and
understanding.
In addition, I wish to thank Dr. Timothy Collins, Dr. Reuben Epstein,
Dr. Jacques Delettrez, Dr. Larry Iwan, Dr. John Kelly, Dr. Semyon Pa-
pernov, Dr. Sean Reagan, Dr. Barukh Yaakobi and all other excellent LLE
scientists and engineers, from whose talent and experience I should have
sampled more.
My sincere gratitude to the whole LLE sta(cid:27) who taught me what a great
work environment this laboratory is; from the people of Omega operations,
through the mechanical engineering department, through the computer sup-
port group, to illustrations and all in between. Special thanks to Sara Bo-
densteiner, the administrative assistant of LLE’s Experimental Division, and
to Barbara Warren, the graduate administrative assistant at the Physics de-
partment, both of whom helped me go smoothly through the administrative
and student life at the university.
I am especially indebted to Dr. Ya(cid:28)m Aglitskiy for his excellent advice
andinvaluablediscussionsonthesubjectofthiswork, theexperimentalsetup
and diagnostics. His pioneering work has been an important guideline to me.
Lastly, but most importantly, I would like to thank my family, my wife
and colleague Violeta for her support and understanding, and my children,
for being the greatest joy and inspiration there is.
v
ABSTRACT
A series of experiments have been conducted to investigate the dynamic over-
pressure stabilization of the ablative Richtmyer-Meshkov (RM) instability in
inertial con(cid:28)nement fusion (ICF) targets during the start-up phase of im-
plosion. Theory and hydrodynamic simulations predict that due to localized
thermal (cid:29)ux variations modulating the dynamic pressure, the components
of the perturbation spectrum at the ablation front oscillate in time. The
oscillation frequency depends on the mode wavenumber, ablation velocity
and density scalelength or ablation front thickness. These predictions were
veri(cid:28)ed on the 30-kJ OMEGA laser facility by measuring the perturbation
amplitudes and frequencies directly, through face-on x-ray radiography. A
high-resolution, Ir-coated Kirkpatrick-Baez microscope, coupled to a high-
current streak tube provided a continuous record of the target areal density
during shock transit, when it is dominated by the evolution of the ablative
µ
RM instability. Planar plastic targets with variable thickness (30-60 m)
λ = 10 − 30 µ
and single mode ( m) perturbations on the front surface were
irradiated by 1.5 ns square UV laser pulses with intensities ranging from
5×1013 W/cm2 4×1014 W/cm2
to . Results clearly indicate a phase reversal
in the evolution of the target areal density perturbations, in agreement with
theory and simulation. The predicted dependence of the oscillation period
on laser intensity and modulation wavelength was veri(cid:28)ed.
Contents vi
CONTENTS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction 1
1.1 Nuclear Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Principles of Controlled Fusion . . . . . . . . . . . . . . . . . . 4
1.3 Direct-Drive ICF Implosion Dynamics: Shock Transit. . . . . . 9
1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . .
2. Hydrodynamic Instabilities in ICF Targets 19
2.1 The Classical and Ablative Rayleigh-Taylor Instability . . . . 20
2.1.1 Rayleigh-Taylor Instability in ICF Targets . . . . . . . 23
2.2 The Classical and Ablative Richtmyer-Meshkov Instability . . 27
2.2.1 Classical Richtmyer-Meshkov Growth. Impulsive Model. 28
2.2.2 Ablative Richtmyer-Meshkov Instability . . . . . . . . 31
2.2.3 Areal Density Perturbations . . . . . . . . . . . . . . . 47
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
. . . . . . . . . . .
3. Experimental Framework and Diagnostics 51
3.1 Motivations and Design of the Experiment . . . . . . . . . . . 51
3.1.1 Face-on X-ray Radiography . . . . . . . . . . . . . . . 51
3.1.2 Motivations and Experimental Requirements . . . . . . 53
Contents vii
3.2 X-Ray Radiographic Diagnostics . . . . . . . . . . . . . . . . . 60
3.3 Streaked X-ray Imager . . . . . . . . . . . . . . . . . . . . . . 61
3.3.1 Kirkpatrick-Baez Microscope . . . . . . . . . . . . . . . 64
3.3.2 High-current, X-ray Streak Camera . . . . . . . . . . . 68
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
. . . . . . . . . . . . . . .
4. Dynamic Overpressure Experiments 78
4.1 Experiments with the X-ray Framing Camera . . . . . . . . . 79
4.2 Experiments with the Streaked Imaging System . . . . . . . . 87
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Conclusions 109
5.1 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.1.1 Ablative RM instability in cryogenic DT, DD or foam
targets . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.1.2 Impulsive loading of target shells. Picket pulses . . . . 114
5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References 120
Appendix 133
A. LinearizedJumpConditionsAcrossaSubsonicAblationFront134
. . . . . . . . . . . .
B. X-ray Framing Camera Characterization 139
B.1 System Response . . . . . . . . . . . . . . . . . . . . . . . . . 139
B.2 Wiener Filter Construction . . . . . . . . . . . . . . . . . . . . 147
Contents viii
. .
C. Kirkpatrick-Baez Microscope: Design and Development 150
C.1 Optical Design . . . . . . . . . . . . . . . . . . . . . . . . . . 152
C.2 Iridium Deposition and Re(cid:29)ectivity Measurements . . . . . . . 159
C.3 Microscope Characterization . . . . . . . . . . . . . . . . . . . 161
C.4 Extended microscope con(cid:28)gurations . . . . . . . . . . . . . . . 164
. . . . . . . . . . . . . . .
D. Mass Ablation Rate Measurements 170
List of Figures ix
LIST OF FIGURES
1.1 Direct drive ICF geometry. The laser energy is deposited in
theplasmacorona, nearthesurfaceofcriticaldensityandthen
transported to the ablating shell by thermal conduction. . . . 11
1.2 Local variations in the dynamic pressure modify the heat (cid:29)ux
at the perturbation peaks (valleys) of the ablation front. This
increases the mass ablation rate at the peaks [40] and reduces
it at the valleys, resulting in reduced perturbations. . . . . . . 15
ρ
2.1 In a gravitational (cid:28)eld, where a heavy (cid:29)uid with density 1 is
ρ
(cid:16)on top(cid:17) of a lighter (cid:29)uid with density 2 the interface is in
unstable equilibrium and any perturbation will grow until the
(cid:29)uids have exchanged places (the potential energy is minimized) 20
2.2 Four distinct regions are identi(cid:28)ed in a planar ICF target dur-
ing the shock transit phase. . . . . . . . . . . . . . . . . . . . 32
υ˜
2.3 The lateral component y of the velocity perturbation behind
p˜
the shock generates local overpressure behind the peak and
−p˜
underpressure behind the valley. The laser beam propa-
gates from right to left. . . . . . . . . . . . . . . . . . . . . . . 36
List of Figures x
η (t)
2.4 Evolution of the shock-front perturbation s for an interface
with single-mode preimposed modulation with initial ampli-
µm λ = 20µm,c = 36µm/ns,M = 6)
tude of 1.75 ( 2 s . . . . . . 40
2.5 Perturbed pressure gradients with opposite orientation (at the
peak and valley) exist between the shock front and the (cid:29)uid
x = x
interface. A mass element at the interface ( a) will be ac-
celerated against this gradient, resulting in perturbation growth. 42
η /η
2.6 Evolution of normalized shock-front perturbation s 0, ab-
η /η
lation front perturbation a 0 and areal density perturba-
δm/ρ η
tion 1 0 for a perturbed foil with single-mode preimposed
(η = 1.75µm,λ = 20µm,c = 36µm/ns,M = 6)
modulation 0 2 s .
a) Classical interface with no thermal conduction. b)Ablation
included in the model. . . . . . . . . . . . . . . . . . . . . . . 48
3.1 CH foil with single-mode perturbations on the front surface is
imaged using face-on, through-foil x-ray radiography. The x
rays are generated by laser beams illuminating a backlighter
target (not shown). . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 The KB-PJX diagnostic: the retractor in extended position
and the PJX air bubble with the lid open. . . . . . . . . . . . 62
3.3 KB-PJX retractor with access lid removed. The microscope
nose cone is visible inside. . . . . . . . . . . . . . . . . . . . . 63
3.4 Principal scheme of a four-mirror KB design. Two dimensional
image is formed by each of the four perpendicular mirror pairs. 64