Thomas M. Antonsen

The role of chaotic orbits in the determination of power spectra of passive scalars

This paper relates properties of the power spectrum of a passive scalar convected by a chaotic fluid flow to the distribution of finite time Lyapunov exponents. The properties considered include the early time evolution of the power spectrum, the late time exponential decay of the scalar variance, and the wave number dependence of the power spectrum in the presence of a source of scalar variance. Theoretical predictions are tested by comparing full numerical solutions of the relevant partial differential equation to solutions of a model system which includes diffusion and involves integrations along the fluid orbits only. The model system is shown to give results in close agreement with the numerical solutions of the full problem. This suggests the possible general utility of the model equations for a broad range of problems involving passive scalar convection.

Stability and confinement of nonrelativistic sheet electron beams with periodic cusped magnetic focusing

Sheet electron beams focused by periodically cusped magnetic (PCM) fields are stable against low‐frequency velocity‐shear instabilities (such as diocotron mode). This is in contrast to more familiar unstable behavior in uniform solenoidal magnetic fields. Two rectangular‐cross‐section magnetic configurations capable of focusing in both transverse dimensions are investigated: (i) a closed‐side two‐plane PCM configuration that is topologically equivalent to conventional round‐cross‐section PPM focusing; and (ii) an open‐side configuration that uses ponderomotive PCM focusing in the vertical plane and simple vzBy Lorentz force focusing in the horizontal plane. Both configurations are capable of stable sheet beam confinement. The open‐side configuration appears more practical both for focusing and for realizing matched (cold) beam conditions in which the beam envelope is free from oscillations. For realistic beams with finite emittance, the existence of a matched cold beam solution implies less emittance grow...

Excitation of terahertz radiation by laser pulses in nonuniform plasma channels

The excitation of terahertz radiation by laser pulses propagating in miniature plasma channels is considered. Generation of radiation by laser pulses in uniform plasmas is generally minimal. However, if one considers propagation in corrugated plasma channels, conditions for radiation generation can be met due to the inhomogeneity of the channel and the presence of guided waves with subluminal phase velocities. It is found that for channels and laser pulses with parameters that can be realized today, energy conversion rates of a fraction of a joule per centimeter can be achieved. Miniature corrugated channels can also be used for creation of THz radiation by bunched electron beams.

QUICKPIC: a highly efficient particle-in-cell code for modeling wakefield acceleration in plasmas

A highly efficient, fully parallelized, fully relativistic, three-dimensional particle-in-cell model for simulating plasma and laser wakefield acceleration is described. The model is based on the quasi-static or frozen field approximation, which reduces a fully three-dimensional electromagnetic field solve and particle push to a two-dimensional field solve and particle push. This is done by calculating the plasma wake assuming that the drive beam and/or laser does not evolve during the time it takes for it to pass a plasma particle. The complete electromagnetic fields of the plasma wake and its associated index of refraction are then used to evolve the drive beam and/or laser using very large time steps. This algorithm reduces the computational time by 2-3 orders of magnitude. Comparison between the new algorithm and conventional fully explicit models (OSTRIS) is presented. The agreement is excellent for problems of interest. Direction for future work is also presented.

Nonlinear reduced fluid equations for toroidal plasmas

Nonlinear reduced fluid equations are derived for studying resistive instabilities in large‐aspect‐ ratio, low‐beta toroidal plasmas. An ordering is developed in which plasma compressibility as well as the poloidal curvature are retained. The nonlinear equations can be linearized and used to reproduce the Mercier criterion in the large‐aspect‐ratio, low‐beta limit. A second set of reduced equations is derived from the Braginskii fluid equations. These equations, which are very similar to the reduced magnetohydrodynamic equations, contain diamagnetic effects as well as parallel transport associated with magnetic fluctuations. Both sets of equations conserve energy exactly.

Theory of intense ion beam acceleration

The application of high voltage pulse power techniques to the production of intense ion beams is of great interest for plasma confinement, plasma heating, and pellet implosion. The main problem is that application of a high voltage to a simple anode–cathode gap will draw both an electron current from the cathode and an ion current from the anode, and the electrons will receive most of the input energy due to their smaller mass. Two methods of efficient intense ion beam production are considered: (1) the magnetically insulated diode and (2) the ’’reflex‐triode’’. The relativistic equilibria, the ion current dependence on accelerating voltage, its dependence on applied magnetic field (in the first method), and its variation due to a velocity distribution of the electrons (in the second method) are determined. For both methods the ion current can be substantially enhanced with respect to the Langmuir–Child current due to the presence of the negative electron space charge. In the case of magnetic insulation t...

The spectrum of fractal dimensions of passively convected scalar gradients in chaotic fluid flows

The passive convection of scalar fields by an incompressible fluid flow in two dimensions is investigated numerically. The prescribed flow is chaotic meaning that nearby fluid elements diverge exponentially with time. The gradient of the convected scalar field is of primary interest, and a measure is defined, reflecting the spatial distribution of the regions having large gradient. The dimension spectrum for this measure is computed by the standard box counting technique, and it is found to be fractal. A recent theory proposes that the fractal structure of the scalar gradient can be related to the nonuniform stretching properties of the flow. Using this theory, the fractal dimension spectrum is computed from the distribution of finite time Lyapunov exponents of the flow, and it is found to be in reasonable agreement with the dimension spectrum computed directly by means of box counting.

Numerical simulation of short laser pulse relativistic self-focusing in underdense plasma

Existing experimental results on relativistic self-focusing are interpreted by means of the particle code WAKE using the ponderomotive approximation to describe the laser–plasma interaction [P. Mora and T. M. Antonsen, Jr., Phys. Plasmas 4, 217 (1997)]. Novel features of the code, such as gas medium ionization and an enhanced paraxial approximation, allow more confidence in data interpretation. Simulations where the pulse power is less or close to the critical value match the experimental data. The transmitted pulse spectrum is shown in this case to shift towards longer wavelengths. The pulse is shown to focus over the vacuum diffraction limit, while the energy is slowly depleted. Simulations of pulses above the critical power match experiment with reduced precision. This can be ascribed to beam filamentation. High energy depletion is expected in this case due to Raman instability.

Communication with a chaotic traveling wave tube microwave generator

Traveling wave tubes (TWTs) are vacuum electronic amplifiers (see Beck, Gittins, and Pierce) that are commonly used for communication in the centimeter wavelength range. Increasing demand for high data flow in wireless communication systems (satellite communication systems are a good example) raises needs for making TWTs more compact and efficient. Motivated by this we suggest a scheme in which a TWT with feedback is operated in a highly nonlinear regime where the device behaves chaotically. The chaos is controlled using small controls. Then, at the receiving end a receiving TWT synchronizes to the chaotic transmitter and amplifies the received signal with nearly no distortion. Results on numerical simulations of the proposed scheme are reported and used to evaluate its effectiveness.

Quasistatic magnetic field generated by a short laser pulse in an underdense plasma

The quasistatic magnetic field generated by short laser pulse in a uniform rarefied plasma is found analytically and compared to that of two-dimensional particle simulations. It is shown that an axisymmetric laser pulse generates an azimuthal magnetic field the structure of which is rather complicated inside the laser pulse body. Behind the pulse in the wake region the magnetic field contains a component that is homogeneous in the longitudinal direction and a component that is oscillating at the wave number 2kp, where kp is the wave number of the plasma wake. Particle simulations confirm the analytical results and are also used to treat the case of high intense laser pulses.