Session BO3: Beams, Instabilities, and Turbulence

Plans for near-term neutralized drift compression experiments

One approach to target heating experiments with space-charge dominated ion beams is to simultaneously longitudinally bunch and transversely focus the beam. Axial compression leading to $\sim $100X current amplification and simultaneous radial focusing have led to encouraging energy deposition approaching, but still short of, intensities required for eV-range target heating experiments. We discuss the status of several improvements and associated beam diagnostics that are under development to reach the higher beam intensities, including: (1) greater axial compression via a higher $\Delta $v/v velocity ramp using a new bunching module; (2) improved centroid control via beam steering dipoles; (3) time-dependent focusing elements to correct considerable chromatic aberrations; and (4) plasma injection improvements to maintain a plasma density always greater than the beam density.   

A space-charge neutralizing plasma channel for an intense beam

Ion bunches have been suggested as an attractive means to heat matter to the warm dense matter, or strongly coupled plasma, regime (Temperature $\sim $ 0.1 to 10 eV). For a K$^{+}$ beam at 0.4 MeV, $\sim $1 J/cm$^{2}$ is required to reach 1 eV in solid Aluminum. Also the pulse duration must be short ($<\sim $ 2 ns) to avoid hydrodynamic cooling. A spot radius $\sim $0.5 mm, and current $\sim $10 A, would enable this flux level and pulse duration. The required current will be achieved by compressing the beam axially. To further increase the beam intensity on target, we will use an 8T solenoid, filled with plasma injected from filtered cathodic arc plasma sources. The Neutralized Drift Compression Experiment at LBNL is intended to test these neutralized focusing techniques with the goal of reaching target temperatures $\sim $0.5 eV. Experimental measurements, including the on-axis plasma density distribution and the beam density distribution, will be presented.   

Improved neutralized compression and focusing of an intense ion beam using a final focus solenoid

Future target heating experiments with space-charge dominated ion beams require simultaneous longitudinal bunching and transverse focusing. We present an experiment to simultaneously focus a singly charged potassium ion beam at LBNL. The space charge of the beam must be neutralized so only emittance limits the focused beam intensity. An induction bunching module provides a head-to-tail velocity ramp upstream of a neutralizing plasma column and a final focusing solenoid. The beam parameters are tuned with a four-solenoid lattice to transport the neutralized compressing beam into a final focus solenoid which transversely focuses the beam at the target plane. We have improved the axial focus ($>$ 100x axial compression, $<$ 2 ns pulses) and reduced the beam spot size. A comparison of experimental and modeling results are presented. (This work was supported by the U.S. D.O.E. under DE-AC02-05H11231 and DE-AC02-76CH3073 for HIFS-VNL)   

Planning for NDCX-II, a next-step platform for ion beam-driven Warm Dense Matter studies

The Heavy Ion Fusion Science Virtual National Laboratory, a collaboration of LBNL, LLNL, and PPPL, has achieved 60-fold temporal pulse compression of ion beams on the Neutralized Drift Compression eXperiment (NDCX) at LBNL. Here, a velocity ``tilt" is imparted to the beam by a ramped voltage pulse as it traverses an induction gap; the beam's tail then catches up with its head in a plasma environment that provides the needed neutralization. Initial studies of matter heated by low-energy ions are beginning on NDCX. We seek to experimentally study uniformly heated foils for basic Warm Dense Matter physics, and key aspects of ion direct drive for inertial fusion. These goals require an improved platform, NDCX-II, and this talk will describe our progress and planning thereof, with an emphasis on simulation studies of beam dynamics.   

Further Development of the Gyrotron- Powered Pellet Accelerator

The Gyrotron-Powered Pellet Accelerator provides an enabling technology to efficiently fuel ITER with fast pellets launched from the High Field Side (HFS) separatrix. Pellet experiments have repeatedly found that fuel efficiently is high - consistent with 100\%. In contrast, Low Field Side (LFS) launch experiments find efficiencies of 50\% or less. This report addresses what experimental program and what material choices can be made to retain program momentum. An initial program seeks to establish that our heterogeneous approach to conductivity works, maintaining s 1 mho/m. A demonstration of acceleration can be carried out in a very simple laboratory when the pusher material D$_2$[Be] is replaced by LiH[C] which is a room temperature solid with a graphite particle suspension. No cryogenics or hazard chemicals. The mm-wave mirror will be graphite, the tamper is sapphire, and the payload LiD. The payload has a pellet has diameter = 3mm and a mass M = 4.4x10$^{-4}$ kg which is 220 joules at V=1000 m/s. A barrel length of 15 cm completes the design specification.   

Electron Beam Focusing Dynamics in Gas-filled Transport Cells for Radiography

At Sandia National Laboratories, investigations of intense electron beam-driven diodes for flash x-ray radiography are being conducted on the RITS-6 accelerator, 9-12 MV. One of several diodes under investigation is the paraxial diode, which employs a gas-filled transport cell to focus the beam onto a high atomic number target to generate x-rays. LSP simulations have shown that the primary limitation in spot size is attributed to the finite decay of the plasma return current which causes the beam focal position to shift axially during the timescale of the pulse, hence leading to an increased radiation spot. Time-resolved measurements of the radiation spot are reported which convey this trend.   

Alignment between velocity and magnetic field fluctuations in the inertial range of solar wind turbulence and comparison to Boldyrev's phenomenological theory

According to Boldyrev's phenomenological theory of incompressible MHD turbulence in a magnetized plasma the cascade of energy and cross-helicity from large to small scales is accompanied by an alignment between the vector velocity and magnetic field fluctuations. This alignment process is governed by the scale-by-scale conservation of energy and cross-helicity and predicts that the angle between $\delta $\textbf{v}$_{\bot }$ and $\delta $\textbf{b}$_{\bot }$ scales like $\lambda ^{1/4}$, where $\lambda $ is the length scale of the fluctuations perpendicular to the mean magnetic field. Solar wind observations show that this scaling law is approximately valid at the largest inertial range scales but breaks down at intermediate to small scales. Analysis of in-situ measurements from the Wind spacecraft at 1 AU are presented and theoretical implications of these results are discussed.   

Theory for the measurement of cascade rates of energy and cross-helicity in axisymmetric incompressible MHD turbulence

A theory is presented for the experimental measurement of the turbulent cascade rates of energy and cross-helicity for incompressible MHD turbulence that is statistically homogeneous and axisymmetric about the mean magnetic field. Like Kolmogorov's four-fifths law for incompressible hydrodynamic turbulence, the theory is based on measurements of third order moments of the fluctuations at two points separated by a vector \textbf{r}. In MHD the third order moments contain combinations of velocity and magnetic field fluctuations and are proportional to the distance r when r lies in the inertial range. For axisymmetric MHD turbulence the third order moments are also functions of the angle $\theta $ between the displacement vector \textbf{r} and the mean magnetic field and the dependence on the angle must be measured to determine the cascade rates from experimental data. Tensor forms for the third order moments in axisymmetric MHD turbulence are derived and the resulting theory reveals an interesting relationship between the cascade rates and the angular dependence of the third order moments.   

Self-organization and criticality of magnetotail plasma

There is a vast observational evidence that magnetic field and plasma fluctuations in the far geo-magnetic tail show a power spectral density that is best modeled by power laws with kinks around some characteristic frequencies. In-situ satellite observations have shown that the fluctuations exhibit scale-free behavior in a range of intermediate and low frequencies but with diverse scaling characteristics. Here we propose a model in which those signatures of scale invariance and power laws are explained in terms of self-organization and criticality of space plasma. In this model the global stability of the tail is provided by the ion component of the plasma, while electrons are attributed the role of a charge-neutralizing background. We discuss the mechanisms of plasma heating and energization in the magnetotail and occurrence of power-law supra-thermal tails in the electron energy distribution. Our model predictions are well inside the range of observational evidence and former theoretical arguments.   

Spatio-temporal dynamics of the magnetosphere: Mutual information function analysis

The magnetospheric response to strong driving by the solar wind is highly structured, and spatially resolved data are essential for the understanding of the spatio-temporal dynamics. The global and local features of the magnetosphere are studied using nonlinear dynamical techniques of phase space reconstruction. A database of the solar wind data from satellites and ground-based magnetometer stations is used to study the magnetospheric response to solar wind variables using mutual information functions. A key feature of the mutual information function is its ability to bring out the linear as well as nonlinear correlations and such functions are needed to study the inherently nonlinear dynamics of the magnetosphere. The spreads in the average mutual information functions computed for the different stations show strong correlations with the solar wind convective electric field and the sudden changes in the dynamic pressure. The time evolution of mutual information shows a westward expansion of the disturbed region in the night side magnetosphere, starting from the near midnight sectors. The mutual information functions are used to quantify the transfer of information among the different locations.   

Extraordinary-Mode Radiation Produced by Linear-Mode Conversion of Langmuir Waves

Linear-mode conversion (LMC) of Langmuir waves to radiation near the plasma frequency at density gradients is important for laboratory, space, and astrophysical phenomena. We study LMC in warm magnetized plasmas using numerical electron fluid simulations when the density gradient is parallel to the ambient magnetic field ($B_0$). We demonstrate that LMC can produce extraordinary ($x$) mode as well as ordinary ($o$) mode radiation from Langmuir waves, contrary to earlier expectations of $o$-mode only. Equal amounts of $o$- and $x$-mode radiation are produced in the unmagnetized limit. The $x$-mode efficiency decreases as $B_0$ increases while the $o$-mode efficiency oscillates due to an interference phenomenon between incoming and reflected Langmuir or $z$-modes. Both $x$- and $o$-mode should be produced for typical coronal and interplanetary parameters, alleviating the long-standing depolarization problem for type III solar radio bursts.   

Instability of coherent whistlers propagating along field lines in the magnetosphere

We report on analytic and simulation studies of nonlinear instability triggered by a whistler propagating along a geomagnetic field line. For simplicity of interpretation, the electron distribution is taken to be the highly unstable ring distribution f(\textbf{v})=$\delta $(v$_{\vert \vert }-$v$_{\vert \vert 0})\delta $(v$_{\bot }-$v$_{\bot 0})$. The variation (quadratic near the equator) of the geomagnetic field B(z) along a field line is important, even though $\lambda \quad \sim $ 1 km while the field gradient scale $\sim $1000 km. The instability is triggered by an initial wave pulse of finite duration $\tau _{p}$; the value of $\tau _{p}$ also plays an important role. Instability occurs initially at the resonant points where $\omega -$kv$_{\vert \vert }-\Omega $=0, but is carried backwards in the pulse by the stream of resonant electrons. The fresh flow of unperturbed electrons into the pulse plays an important role, and in the non-uniform B(z), phase-trapped electrons can continue to drive the nonlinear stage of the instability, which is characterized by both growth and strong spatio-temporal variations of the wave frequency.   

Interaction of electric field with plasma clouds in lower ionosphere

At the lower-E/upper-D altitudes between 80 and 120 km, the ionospheric plasma density is low, especially at nighttime. At these altitudes, meteor plasma trails and sporadic-E layers are often present. The former, highly elongated and slowly diffusing structures have the lengths of several kilometers, the lifetimes from 1s to several minutes, and they fill the entire lower ionosphere. The latter, pancake-like clouds are much rarer, but they span tens to thousands of kilometers in horizontal direction and live several hours and longer. In the lower ionosphere, especially at high latitudes or near the magnetic equator, an external electric field often occurs. This field polarizes the highly conducting clouds, redistributes the electrostatic potential, and generates currents both within and around the cloud. Using a universal approach, we have developed a 3D analytical theory of these phenomena. The theory predicts significant amplification of the electric field in the near-cloud region and strong currents. This is important for generation of plasma instabilities, electron heating, and magnetosphere-ionosphere coupling.   

Modeling Plasma Interactions with Satellite-Borne Instrumentation

We have developed a simulation of ion interactions with the biased grids of the Retarding Potential Analyzer (RPA), which is one of the fundamental instruments of space science. RPAs have successfully been flown on spacecraft since the late 1950's, including Sputnik III, the Viking lander, and the DMSP family of satellites. The RPA measures the distribution of particle flux as a function of ion energy by using biased grids as an energy filter for collected particles. In order to fit collected data to physical parameters, the interaction of charged particles with the biased grid must be studied thoroughly. We have simulated this interaction using ANSYS, a multiphysics software tool. Perturbations to the Whipple RPA equation due to non-uniform potential will be discussed with the intent of developing quantitative corrections to inferred parameters, such as velocity and temperature.   

Dominant unstable mode in fast electron beam plasma interaction

The interaction of a relativistic electron beam with a plasma is a subject of relevance for the Fast Ignition Scenario as well as many astrophysical settings. It has been known for long that the system is unstable with respect to many electromagnetic instabilities such as the two-stream or the filamentation instabilities. Nevertheless, recent theoretical [1] and numerical [2] investigations accounting for the whole unstable wave vector spectrum have highlighted the role of unstable modes with vector aligned obliquely with respect to the beam. In the cold fluid limit, it was proved [3] that the relativistic beam plasma system can be governed by filamentation or oblique instabilities, depending on the beam to plasma density ratio and the beam gamma factor. We here present a full kinetic extension of this previous work accounting for relativistic Maxwell-J\"{u}ttner distributions functions for the beam and the plasma return current. We find that depending on the system parameters, filamentation, oblique and even two-stream modes can govern the system. Some of the implications are discussed. [1] A. Bret, M.-C. Firpo, C. Deutsch, PRL, 94, 115002, 2005. [2] L. Gremillet et. al., 14, 040704, 2007; M.E. Dieckman et. al., PoP, 13, 112110, 2006. [3] A. Bret, C. Deutsch, PoP, 12, 082704, 2005.