Undamped electrostatic plasma waves

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named {\it corner modes}. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the $(k,\omega_{_R})$ plane ($\omega_{_R}$ being the real part of the wave frequency and $k$ the wavenumber), away from the well-known `thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower $k$-values and chopping the tail shifts them toward higher $k$-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.Comment: 11 pages, 10 figure

Plasma diagnostic reflectometry

Theoretical and experimental studies of plasma diagnostic reflectometry have been undertaken as a collaborative research project between the Lawrence Livermore National Laboratory (LLNL) and the University of California Department of Applied Science Plasma Diagnostics Group under the auspices of the Laboratory Directed Research and Development Program at LLNL. Theoretical analyses have explored the basic principles of reflectometry to understand its limitations, to address specific gaps in the understanding of reflectometry measurements in laboratory experiments, and to explore extensions of reflectometry such as ultra-short-pulse reflectometry. The theory has supported basic laboratory reflectometry experiments where reflectometry measurements can be corroborated by independent diagnostic measurements

Pinhole closure measurements

Spatial-filter pinholes and knife-edge samples were irradiated in vacuum by 1053-nm, 5-20 ns pulses at intensities to 500 GW/cm. The knife-edge samples were fabricated of plastic, carbon, ahnuinum, stainless steel, molybdenum, tantalum, gold and an absorbing glass. Time-resolved two-beam interferometry with a 40-ns probe pulse was used to observe phase shifts in the expanding laser-induced plasma. For all of these materials, at any time during square-pulse irradiation, the phase shift fell exponentially with distance from the edge of the sample. The expansion was characterized by the propagation velocity V2x of the contour for a 2(pi) phase shift. To within experimental error, V2x, was constant during irradiation at a particular intensity, and it increased linearly with intensity for intensities 2. For metal samples, V, exhibited an approximate M-0.5 dependence where M is the atomic mass. Plasmas of plastic, carbon and absorbing glass produced larger phase shifts, and expanded more rapidly, than plasmas of the heavy metals. The probe beam and interferometer were also used to observe the closing of pinholes. With planar pinholes, accumulation of on-axis plasma was observed along with the advance of plasma away from the edge of the hole. On-axis closure was not observed in square, 4-leaf pinholes

Achievement of target gain larger than unity in an inertial fusion experiment.

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G_{target} of 1.5. This is the first laboratory demonstration of exceeding "scientific breakeven" (or G_{target}>1) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the Lawson criterion for fusion ignition as reported in a previous NIF implosion [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129, 075001 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.075001]. This achievement is the culmination of more than five decades of research and gives proof that laboratory fusion, based on fundamental physics principles, is possible. This Letter reports on the target, laser, design, and experimental advancements that led to this result

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Vlasov on GPU (VOG project)******

This work concerns the numerical simulation of the Vlasov-Poisson equation using semi-Lagrangian methods on Graphics Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented. First and foremost, a reformulation of semi-Lagrangian methods is performed, which enables us to rewrite the governing equations as a circulant matrix operating on the vector of unknowns. This product calculation can be performed efficiently using FFT routines. Nowadays GPU is no more limited to single precision; however, single precision may still be preferred with respect to performance and available memory. So, in order to be able to deal with single precision, a δf type method is adopted which only needs refinement in specialized areas of phase space but not throughout. Thus, a GPU Vlasov-Poisson solver can indeed perform high precision simulations (since it uses very high order of reconstruction and a large number of grid points in phase space). We show results for more academic test cases and also for physically relevant phenomena such as the bump on tail instability and the simulation of Kinetic Electrostatic Electron Nonlinear (KEEN) waves

A numerical study of ultra-short-pulse reflectometry

Ultra-short-pulse reflectometry is studied by means of the numerical integration of a one-dimensional full-wave equation for ordinary modes propagating in a plasma. The numerical calculations illustrate the potential of using the reflection of ultra-short-pulse, microwaves as an effective probe of the density profile even in the presence of significant density fluctuations. The difference in time delays of differing frequency components of the microwaves can be used to deduce the density profile. The modification of the reflected pulses in the presence of density fluctuations is examined and can be understood based on considerations of Bragg resonance. A simple and effective profile-reconstruction algorithm using the zero-crossings of the reflected pulse and subsequent Abel inversion is demonstrated. The robustness of the profile reconstruction algorithm in the presence of a sufficiently small amplitude density perturbation is assessed