We present direct-drive target design studies for the laser mégajoule using two distinct initial aspect ratios (A = 34 and A = 5). Laser pulse shapes are optimized by a random walk method and drive power variations are used to cover a wide variety of implosion velocities between 260 km/s and 365 km/s. For selected implosion velocities and for each initial aspect ratio, scaled-target families are built in order to find self-ignition threshold. High-gain shock ignition is also investigated in the context of Laser MégaJoule for marginally igniting targets below their own self-ignition threshold

Brandon, V.

Canaud, B.

Laffite, S.

Ramis Abril, Rafael

Temporal, Mauro

V. Brandon

B. Canaud

S. Laffite

M. Temporal

R. Ramis

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Systematic analysis of direct-drive baseline designs for shock ignition with the Laser MégaJoule

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EPJ Web of Conferences 59, 03004 (2013)
DOI: 10.1051/epjconf/20135903004
C© Owned by the authors, published by EDP Sciences, 2013
Systematic analysis of direct-drive baseline designs for
shock ignition with the Laser MégaJoule
V. Brandon1, B. Canaud1,a, S. Laffite1, M. Temporal2 and R. Ramis2
1CEA, DAM, DIF, 91297 Arpajon, France
2ETSIA, Universidad Politécnica de Madrid, Spain
Abstract. We present direct-drive target design studies for the laser mégajoule using two distinct initial
aspect ratios (A = 34 and A = 5). Laser pulse shapes are optimized by a random walk method and drive
power variations are used to cover a wide variety of implosion velocities between 260 km/s and 365 km/s.
For selected implosion velocities and for each initial aspect ratio, scaled-target families are built in order to
find self-ignition threshold. High-gain shock ignition is also investigated in the context of Laser MégaJoule
for marginally igniting targets below their own self-ignition threshold.
1. INTRODUCTION
Inertial confinement fusion (ICF) consists in illuminating a shell of fusible fuel with laser beams in
direct-drive approach [1] or with x-ray in indirect drive approach [2]. Two laser facilities are built to
achieve ICF with indirect drive configuration: the National Ignition Facility (NIF) in U.S.A. [3] and
the Laser MégaJoule (LMJ) in France [4]. For LMJ, directly-driven self-ignition is possible [1] with
indirect-drive beam geometry with zooming [5]. Moreover, Shock Ignition (SI) [6] and its application
on LMJ [7] bring a new interest for direct-drive approach because it can offer high gain for non self-
igniting target and allows to investigate the self-ignition threshold [8]. In this scheme, compression
phase and ignition are separated. Usually, targets designs present high initial aspect ratio A, defined as
the ratio of the deuterium-tritium (DT) ice-layer inner radius over the DT-ice layer thickness, around
A = 7 for Fast-Ignition (FI) [9] or for Direct-Drive (DD) targets [1] and around A = 11 for indirect
drive targets [4]. In our study, we explore low initial aspect ratios and moderate implosion velocities.
Targets and laser pulses are optimized by a random-walk method and drive power variations in order
to vary the implosion velocity. Then, selected target designs are scaled in Sec. 4 in order to scan the
self-ignition threshold of transition between non- or marginally-igniting targets and burning targets, and
finally shock ignition of marginally igniting targets at low implosion velocities is investigated.
2. DIRECT-DRIVE BASELINE DESIGNS
We set A = 3 and 5. Targets and laser pulses are described in Fig. 1. The initial aspect ratio considers
only the 300 g-DT ice-layer assuming that the polyimide (CH) ablator is fully expanded at the end
of the laser pulse. CH ablator thickness and drive power are initially given by Rocket-effect formulae
[2] for an implosion velocity of 310 km/s and assuming full ablation of CH. Calculations are then
performed using the one-dimensional (1D) Lagrangian radiation-hydrodynamics code FCI1 [10]. Laser
pulse shapes are initially defined to achieve implosion velocities around 310 km/s for each design and
ae-mail: benoit.canaud@cea.fr
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20135903004
EPJ Web of Conferences
Figure 1. Targets designs (left) with A = 3 (left-green) and A = 5 (right-yellow) and laser pulses (right).
Figure 2. Thermonuclear energy versus implosion velocity for A = 3 (left) and A = 5 (right). Colored points are
given in Table 1.
follow a Kidder-like law [11] to minimize entropy during the whole compression phase. The foot is
chosen to get an inflight adiabat of one in the fuel layer. Drive duration is constant in our study and is
sized to correspond to the ablator thickness with laser power drive of 100 TW. This first optimization
is complemented by a random-walk method that consists in varying the pulse ramp in order to obtain
a refined shock timing that maximizes the areal density at stagnation of non-igniting targets or the
thermonuclear energy when target ignites. The drive power also varies. A new laser pulse is built for
each random realization. Successive refinements of intervals are used to cover unexplored part of the
parameter space and to get an optimum. The results are shown in Fig. 2 where thermonuclear energy is
given versus implosion velocity for each aspect ratio. Each dot represents a 1D-implosion. Self ignition
threshold is observed for an implosion velocity of 300 km/s for A = 3, and 325 km/s for A = 5. Thus,
with the same fuel mass, the self-ignition kinetic-threshold is lower for A = 3 than for A = 5. We notice
that the absorbed laser energy is higher for A = 3 than for A = 5 for the same implosion velocity. Thus
the thermonuclear gain, above ignition, is roughly the same for both aspect ratios but not at the same
implosion velocity (cf Table1).
3. SCALED TARGETS
We selected a few designs at the frontier of the data clouds for both A that are marked by colored
points in Fig. 2. These points, summarized in Table 1, offer the maximum areal density (under self
ignition threshold) or maximum thermonuclear energy (above self ignition threshold), with minimum
absorbed energy for different implosion velocities. The average peak areal density is higher for A = 3
(r  19 kg/m2) than for A = 5 (r  16 kg/cm2). An Eulerian scaling [12] is applied to the previous
set of designs that conserves velocities and laser intensities to explore thermonuclear energy as a
03004-p.2
IFSA 2011
Table 1. List of working points selected to compute scaled targets.
A = 3 A = 5
V Ea R Eth V Ea R Eth
(km/s) (kJ) (kg/m2) (kJ) (km/s) (kJ) (kg/m2) (kJ)
280 171 1.46 12
286 215 18.5 18 289 181 15.0 21
294 233 18.8 15 294 187 15.3 25
297 238 18.4 29 298 193 15.6 32
306 234 18.6 573 303 199 15.8 49
308 250 18.7 8389 308 204 15.9 44
314 260 18.2 23032
320 272 18.6 26216 317 219 16 234
325 283 18.9 26915 329 226 16 18 119
333 233 16.4 21 411
348 249 16.6 24 862
352 264 16.4 25 064
356 267 16.6 25 695
365 280 16.7 26 296
Figure 3. Thermonuclear energy as function of kinetic energy for A = 3 (left) and A = 5 (right). Each curve is
scaled from a selected point described in Table 1.
function of kinetic energy (cf Fig. 3). Scaling laws are expressed in function of a scale factor f:
m1/m0 = f , E1/E0 = f , r1/r0 = f 1/3, t1/t0 = f 1/3, Plaser 1/Plaser 0 = f 2/3, V1/V0 = 1, 1/0 = 1,
and I1/I0 = 1. Self-ignition is always achieved for all curves with a kinetic self-ignition threshold which
decreases with the implosion velocity. Such preliminary results are very promising and will be deeply
detailed in a future article.
4. SHOCK IGNITION
The shock ignition scheme [6] consists in adding a high power spike at the end of the drive pulse.
This spike creates a strong shock that propagates towards the hot spot which departs from an isobaric
stagnation, and reduces the ignition threshold. Spike timing must be adjusted in function of the spike
power as shown in Fig. 4. This approach is applied to a marginally-igniting target that is under its self-
ignition threshold for A = 5 and v = 317 km/s (here, f = 0.7). Figure 4 represents the ignition window.
Thermonuclear gain (∼90), defined as the ratio of thermonuclear energy over the absorbed energy, is
exactly the same as the one obtained for the self-igniting target, when f = 1. Indeed, thermonuclear
energy is roughly 17 MJ for 180 kJ of absorbed energy and a DT-mass of 210 g.
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EPJ Web of Conferences
Figure 4. 1D gain versus spike power and time-of-launch for A = 5, f = 0.7, and V = 317 km/s.
5. CONCLUSION
We present preliminary results about two new families of target designs with initial aspect ratios A of 3
and 5. A large range of peak implosion velocities is explored by the means of a random walk method.
Self-ignition is obtained at a higher implosion velocity for A = 5 than for A = 3. Selected points are
identified that maximize thermonuclear energy and peak areal densities for given absorbed energies.
Scaling laws that conserve implosion velocities are applied to this set of selected designs that allow to
compose a large library of target designs in function of initial aspect ratio, peak implosion velocity, fuel
mass and position relative to self-ignition threshold. Finally, shock ignition is considered for a reduced-
size marginally-igniting target that produces a 1D gain of 93.
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