Retracted

**Optical polarizer/isolator based on a rectangular waveguide with helical grooves**

G. Shvets

**Abstract**

A chirality-based approach to making a one-way waveguide that can be used as an optical isolator or a polarizer is described. The waveguide is rectangular, and chirality is introduced by making slanted rectangular grooves on the waveguide walls. Chirality of the waveguide manifests as a strong circular dichroism and is responsible for transmitting one circular polarization of light and reflecting the other. Optical isolation of the propagating circular polarization is accomplished when the chiral waveguide is placed in front of a nonchiral optical device. Even the crudest implementations of chirality are shown to exhibit significant circular dichroism. *©2006 American Institute of Physics *

DOI:10.1063/1.2355466

**Breakup of shearless meanders and "outer" tori in the standard nontwist map **

K. Fuchss, A. Wurm, A. Apte, P.J. Morrison

**Abstract**

The breakup of shearless invariant tori with winding number ω=(11+γ)/(12+γ) (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number can assume the shape of meanders [folded-over invariant tori which are not graphs over the x axis in (x,y) phase space], whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated. *©2006 American Institute of Physics *

DOI:10.1063/1.2338026

**A comparison of sawtooth oscillations in bean and oval shaped plasmas **

E A Lazarus, F L Waelbroeck, T C Luce, M E Austin, K H Burrell, J R Ferron, A W Hyatt, T H Osborne, M S Chu, D P Brennan, P Gohil, R J Groebner, C L Hsieh, R J Jayakumar, L L Lao, J Lohr, M A Makowski, C C Petty, P A Politzer, R Prater, T L Rhodes, J T Scoville, E J Strait, A D Turnbull, M R Wade, G Wang, H Reimerdes and C Zhang

**Abstract**

The effect of plasma shape on sawtooth oscillations in the DIII-D tokamak plasmas is investigated by comparing discharges with cross-sections shaped like a bean and an oval. The two shapes are designed so that the Mercier instability threshold is reached when the axial safety factor is below unity for the bean and above unity for the oval cross-sections. This allows the role of interchange modes to be differentiated from that of the kink-tearing mode. The differences in the nature of the sawtooth oscillations in the bean and oval discharges are found to be determined primarily by extreme differences in the electron heat transport during the reheat. In both cases, the axial safety factor is found to be near unity following the crash. *©2006 IOP Publishing Ltd. *

DOI: 10.1088/0741-3335/48/8/L01

**Equilibrium, multistability, and chiral asymmetry in rotated mirror plasmas **

P.M. Valanju, S.M. Mahajan, H.J. Quevedo

**Abstract**

The Hall term in two-fluid magnetohydrodynamics is shown to be necessary to balance the curl of the ion inertial force in a rotating plasma with spatially nonuniform crossed electric and magnetic fields. Two-fluid solutions are obtained that qualitatively explain the multistable rotational response observed in magneto-Bernoulli experiment, imply chiral symmetry breaking, i.e., handedness, and yield new dynamo-like electromotive terms in the effective circuit equation for externally rotated mirror plasma equilibria.*©2006 American Institute of Physics *

DOI:10.1063/1.2209967

**Stability of the resistive wall mode in HBT-EP plasmas **

R. Fitzpatrick, J. Bialek

**Abstract**

A relatively simple model of the resistive wall mode (RWM) is derived for a large aspect ratio, low β, circular cross section, tokamak plasma, surrounded by a concentric, thin, uniform resistive wall. The model employs uniform toroidal plasma rotation, and includes the following realistic edge dissipation mechanisms: dissipation due to charge-exchange with cold neutrals, and dissipation due to neoclassical flow damping. The model is applied to the HBT-EP tokamak [T. Ivers, E. Eisner, A. Garofalo et al., Phys. Plasmas 3, 1926 (1996)], with the wall parameters determined by fitting to output from the VALEN code [J. Bialek, A. H. Boozer, M. E. Mauel, and G. A. Navratil, Phys. Plasmas 8, 2170 (2001)]. Dissipation due to charge-exchange with cold neutrals is found to be not quite large enough to account for the observed rotational stabilization of the RWM in HBT-EP plasmas. On the other hand, dissipation due to neoclassical flow damping is sufficiently large to explain the observations. *©2006 American Institute of Physics *

DOI:10.1063/1.2245542

**Weak effect of ion cyclotron acceleration on rapidly chirping beam-driven instabilities in the National Spherical Torus Experiment **

W.W. Heidbrink, E. Ruskov, E.D. Fredrickson, N. Gorelenkov, S.S. Medley, H.L. Berk, R.W. Harvey

**Abstract**

The fast-ion distribution function in the National Spherical Torus Experiment is modified from shot to shot while keeping the total injected power at ~2 MW. Deuterium beams of different energy and tangency radius are injected into helium L-mode plasmas, producing a rich set of instabilities, including compressional Alfvén eigenmodes, toroidicity-induced Alfvén eigenmodes (TAE), 50–100 kHz instabilities with rapid frequency sweeps or chirps, and strong, low frequency (10–20 kHz) fishbones. The experiment was motivated by a theory that attributes frequency chirping to the formation of holes and clumps in phase-space. In the theory, increasing the effective collision frequency of the fast ions that drive the instability can suppress frequency chirping. In the experiment, high-power (approximately less-than 3 MW) high harmonic fast wave (HHFW) heating accelerates the fast ions in an attempt to alter the nonlinear dynamics. Steady-frequency TAE modes diminish during the HHFW heating but there is little evidence that frequency chirping is suppressed. *©2006 IOP Publishing Ltd. *

DOI: 10.1088/0741-3335/48/9/006

**Self-sustaining vortex perturbations in smooth shear flows **

J.-H. Kim, J.C. Perez, W. Horton, G.D. Chagelishvili, R.G. Changishvili, J.G. Lominadze, John C. Bowman

**Abstract**

The nonlinear dynamics of coherent circular/elliptical cyclonic and anticyclonic vortices in plane flow with constant shear is investigated numerically using a dealiased Fourier pseudospectral code. The flow is asymptotically linearly stable, but is highly non-normal, allowing perturbations to gain energy transiently from the background shear flow. This linear transient growth interplays with nonlinear processes. In certain cases it is shown that the nonlinear feedback is positive, leading to self-sustaining coherent vortices. Self-sustaining coherent vortices exist where the vorticity is parallel to the mean flow vorticity (cyclonic rotation). The required nonlinear feedback is absent for small amplitude anticyclonic vortices. However, elliptical anticyclonic vortices become self-sustaining if the amplitude exceeds a threshold value. The self-sustaining of coherent vortices is similar to the subcritical, so-called bypass, transition to turbulence in shear flows. The common features are: transient linear growth; positive nonlinear feedback; and anisotropy of the linear and nonlinear phenomena (in contrast to isotropic Kolmogorov turbulence). A plasma laboratory experiment is suggested based on the results of this investigation. *©2006 American Institute of Physics *

DOI:10.1063/1.2209229

**IFSR-1167**

**Proper performance prediction for ITER **

R.J. Goldston, R.D. Hazeltine

Physics Today; Jun2006, Vol. 59 Issue 6, p11-12, 2p

**Abstract**

A letter to the editor is presented in response to an article by David Montgomery which expressed concern about the theoretical basis for predicting the performance of ITER, the planned international magnetic fusion energy experiment. *© Physics Today*

**Applications of noise theory to plasma fluctuations **

B. Li, R.D. Hazeltine

**Abstract**

Noise theory is used to study the temporal correlations of stationary random fluctuations that are homogeneous in space. Statistical properties of the fluctuations, such as the power spectrum and the correlation function, are computed. The results are compared with the observed plasma density fluctuations from tokamak experiments.*©2006 The American Physical Society*

DOI: 10.1103/PhysRevE.73.065402

**Revisiting the anomalous RF field penetration into a warm plasma **

I.D. Kaganovich, O.V. Polomarov, C.E. Theodosiou

**Abstract**

Radio frequency waves do not penetrate into a plasma and are damped within it. The electric field of the wave and plasma current are concentrated near the plasma boundary in a skin layer. Electrons can transport the plasma current away from the skin layer due to their thermal motion. As a result, the width of the skin layer increases when electron temperature effects are taken into account. This phenomenon is called anomalous skin effect. The anomalous penetration of the rf electric field occurs not only for transversely propagating to the plasma boundary wave (inductively coupled plasmas) but also for the wave propagating along the plasma boundary (capacitively coupled plasmas). Such anomalous penetration of the rf field modifies the structure of the capacitive sheath. Recent advances in the nonlinear, nonlocal theory of the capacitive sheath are reported. It is shown that separating the electric field profile into exponential and non-exponential parts yields an efficient qualitative and quantitative description of the anomalous skin effect in both inductively and capacitively coupled plasma. *© 2006 IEEE*

DOI: 10.1109/TPS.2006.873253

**Self-consistent modeling of nonlocal inductively coupled plasmas **

O.V. Polomarov, C.E. Theodosiou, I.D. Kaganovich, D.J. Economou, B.N. Ramamurthi

**Abstract**

In low-pressure radio-frequency (RF) discharges, the electron-energy distribution function (EEDF) is typically non-Maxwellian for low plasma density. The nonlocal plasma conductivity, plasma density profiles, and EEDF are all nonlinear and nonlocally coupled. For accurate calculation of the discharge characteristics, the EEDF needs to be computed self-consistently. The method of fast self-consistent one-dimensional of planar inductively coupled discharges driven by a RF electromagnetic field is presented. The effects of a non-Maxwellian EEDF, plasma nonuniformity, and finite size, as well as the influence of the external magnetic field on the plasma properties are considered and discussed.*© 2006 IEEE*

DOI:10.1109/TPS.2006.875733

**Observation and explanation of the JET n=0 chirping mode **

C.J. Boswell, H.L. Berk, D.N. Borba, T. Johnson, S.D. Pinches, S.E. Sharapov

Physcis Letters A Volume 358, Issue 2, 9 October 2006, Pages 154-158

**Abstract**

Persistent rapid up and down frequency chirping modes with a toroidal mode number of zero (n=0) have been observed in the JET tokamak when energetic ions, with a mean energy ~500 keV, were created by high field side ion cyclotron resonance frequency heating. This heating method enables the formation of an energetically inverted ion distribution function that allows ions to spontaneously excite the observed instability, identified as a global geodesic acoustic mode. The interpretation is that phase space structures form and interact with the fluid zonal flow to produce the pronounced frequency chirping.© *2006 Elsevier B.V.*

DOI:10.1016/j.physleta.2006.05.030

**Interpretation of core localized Alfven eigenmodes in DIII-D and Joint European Torus reversed magnetic shear plasmas **

G.J. Kramer, R. Nazikian, B. Alper, M. de Baar, H.L. Berk, G.Y. Fu, N.N. Gorelenkov, G. McKee, S.D. Pinches, T.L. Rhodes, S.E. Sharapov, W.M. Solomon, M.A. van Zeeland

**Abstact**

Reversed shear Alfvén eigenmodes (RSAE) that were observed in the Joint European Torus (JET) [P. H. Rebut and B. E. Keen, Fusion Technol.11, 13 (1987)] and DIII-D [J. L. Luxon, Nucl. Fusion42, 614 (2002)] are studied with the ideal magnetohydrodynamic code NOVA-K [C. Z. Cheng, Phys. Rep.211, 1 (1992)]. It was found that the frequency behavior of the RSAEs can be described accurately by the NOVA-K code when plasma compressibility effects and toroidal plasma rotation are taken into account. For the mode activity on JET, the calculated drive exceeds the mode damping rate, consistent with experimental observations, while on DIII-D the growth rate from neutral beam ions for modes with high toroidal mode numbers is insufficient to account for the excitation of the modes and a major part of the drive comes from the background plasma. *©2006 American Institute of Physics *

DOI:10.1063/1.2186049

**Effects of pressure gradient on existence of Alfvén cascade modes in reversed shear tokamak plasmas **

G.Y. Fu, H.L. Berk

**Abstract**

It is shown analytically that pressure gradient effects are favorable to the existence of Alfvén cascade (AC) modes in a tokamak plasma with reversed shear. What is crucial for obtaining the improved existence criterion of ACs is the averaged normal curvature. This term depends on the Shafranov shift, which contains a pressure gradient term that at sufficiently low frequency causes a cancellation in the mode existence criterion of all terms quadratic in the pressure gradient. The favorable criterion is then found to be proportional to the product of the pressure gradient and the inverse aspect ratio. Near the rational surface, there is one-to-one correspondence between Mercier stability and the AC mode existence. When the averaged curvature is favorable to Mercier modes, it is also favorable to the existence of AC. However, at higher frequencies the α^{2} term can be unfavorable to mode existence. We show that when α>3ε, that as *q*_{min} decreases from *m/n*, the cascade mode can easily satisfy its existence criterion at lower frequencies, but the existence criterion will fail before the frequency reaches the toroidal Alfvén eigenmode (TAE) gap, which occurs when *q*_{min} approaches (m–1/2)/n. *©2006 American Institute of Physics *

DOI:10.1063/1.2196246

**Drift-magnetohydrodynamical model of error-field penetration in tokamak plasmas**

A. Cole, R. Fitzpatrick

**Abstract**

A previously published magnetohydrodynamical (MHD) model of error-field penetration in tokamak plasmas is extended to take drift-MHD physics into account. In particular, diamagnetic and semicollisional effects are both fully incorporated into the analysis. The new model is used to examine the scaling of the penetration threshold in ohmic tokamak plasmas. *©2006 American Institute of Physics *

DOI:10.1063/1.2178167

**Propagation of radially localized helicon waves in longitudinally nonuniform plasmas **

A.V. Arefiev, B.N. Breizman

**Abstract**

A gradient in the plasma density across the guiding magnetic field can support a low-frequency radially localized helicon (RLH) wave in a plasma column. If the radial density gradient changes along the magnetic field, this wave can undergo reflection and also excite conventional whistlers. This paper presents calculations of the corresponding reflection coefficient, including the effect of whistler radiation. It is shown that a sharp longitudinal density drop causes a nearly complete reflection of the RLH wave. The longitudinal wavelength of the excited whistlers is much greater than that of the RLH wave, and, as a result, only a small fraction of the RLH wave energy is transferred to the whistlers. *©2006 American Institute of Physics*

DOI:10.1063/1.2212367

**Adiabatic bistable evolution of dynamical systems governed by a Hamiltonian with separatrix crossing**

O. Polomarov, G. Shvets

**Abstract**

Adiabatic evolution of a nonlinear resonantly driven dynamical system generic to a variety of plasma physics problems is studied. The corresponding Hamiltonian, depending on the strength and frequency of the slowly varying driver, has a variable number of fixed points and the dynamical system can be bistable due to repeated separatrix crossing in the phase space. It is analytically shown that the oscillation periods along the "sister" trajectories corresponding to the same value of the Hamiltonian are equal and the sum of the corresponding areas under them does not depend on the driver amplitude. As a consequence of that, the Hamiltonian of a bistable system always follows the same trajectory for an adiabatically varying driver, regardless of whether the system is excited or left quiescent. *© 2006 American Institute of Physics*

DOI: 10.1063/1.2201927

**The dynamics of storms and substorms with the WINDMI model**

E. Spencer, W. Horton, I. Doxas

Advances in Space Research, Volume 38, Issue 8, 2006, Pages 1657-1668

**Abstract**

WINDMI is a physics based eight-dimensional state-space model that simulates the flow of energy between the dominant global energy components in the nightside magnetosphere. The model is intrinsically three-dimensional in configuration space, and uses the basic geometry of the Tsyganenko magnetic field model to define the physical quantities. The dynamical equations satisfy the laws of energy and charge conservation for the network of branches and nodes formed by the topology of the ambient magnetic field. The model includes energy coupled by injected plasma from the plasma sheet across the Alfvén layer into the ring current. The power input into the model is the electromotive plasma dynamo derived from solar wind parameters. The output of the model is the westward Auroral Electrojet current and the energy stored in the Earth’s ring current. The prediction of the model is compared to the geomagnetic AL and D_{st} indices. These indices measure fluctuations of the earth’s magnetic field at its surface. The model parameters have been optimized using a genetic algorithm with the Average Relative Variance (ARV) as a performance metric for five of the seven designated Geospace Environment (GEM) storms. Results for the October 3–7 2000 GEM storm and the October 20–22 2001 GEM storm are given here. The optimized models appear to give a reliable method of making predictions from the solar wind for a range of auroral and ring current activity. *© 2006 COSPAR. Published by Elsevier Ltd.*

DOI:
10.1016/j.asr.2006.02.013

**Hamiltonian structure of a collisionless reconnection model valid for high and low Β plasmas**

E. Tassi, P. J. Morrison, D. Grasso

**Abstract**

The noncanonical Hamiltonian formulation of a recently derived four-field model describing collisionless reconnection is presented. The corresponding Lie-Poisson bracket is shown to be a sum of a direct and semi-direct product forms and to possess four infinite independent families of Casimir invariants. Three out of four of these families are directly associated with the existence of Lagrangian invariants of the model. Two of the invariants generalize previously discovered invariants of a two-field model for reconnection in low-Β plasmas. Finally a variational principle is given for deriving general equilibrium equations and an example of an equilibrium solution is described explicitly.

**A unified approach to the Darwin approximation**

T.B. Krause, P.J. Morrison, A. Apte

**Abstract**

There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting.* © 2007 American Institute of Physics*

DOI:10.1063/1.2799346

**Relating parallel and perpendicular flows of particles and heat in a magnetized toroidal plasma **

Abinadab Dieter, R. D. Hazeltine

**Abstract **

The purpose of this Brief Communication is to emphasize the existence of a general relation between the parallel flows of heat and particles within flux surfaces and the transport of heat and particles across those flux surfaces predicted by neoclassical theory. The essential ingredients are a perspective that promotes the heat flow to the status of a fully independent dynamical variable and a unified treatment that makes no restriction regarding collisionality. Applied to well-known expressions from the literature, this approach provides a simple and explicit relation between parallel and radial flows that applies in all collisionality regimes. *©2006 American Institute of Physics*

DOI: 10.1063/1.2338821

**Fast particle interaction with waves in fusion plasmas **

B.N. Breizman

**Abstract**

There are two well-known motivations for theoretical studies of fast particle interaction with waves in magnetic confinement devices. One is the challenge of avoiding strong collective losses of alpha particles and beam ions in future burning plasma experiments. The other one is the compelling need to quantitatively interpret the large amount of experimental data from JET, TFTR, JT-60U, DIII-D, and other machines. Such interpretation involves unique diagnostic opportunities offered by MHD spectroscopy. This report discusses how the present theory responds to the stated challenges and what theoretical and computational advances are required to address the outstanding problems. More specifically, this paper deals with the following topics: predictive capabilities of linear theory and simulations; theory of Alfvén cascades; diagnostic opportunities based on linear and nonlinear properties of unstable modes; interplay of kinetic and fluid nonlinearities; fast chirping phenomena for non-perturbative modes; and global transport of fast particles. Recent results are presented on some of the listed topics, although the main goal is to identify critical issues for future work. *© 2006 American Institute of Physics*

DOI:10.1063/1.2404536

**Resonant power absorption in helicon plasma sources **

G. Chen, A. Arefiev, R.D. Bengtson, B.N. Breizman, C.A. Lee, L.L. Raja

**Abstract**

Helicon discharges produce plasmas with a density gradient across the confining magnetic field. Such plasmas can create a radial potential well for nonaxisymmetric whistlers, allowing radially localized helicon (RLH) waves. This work presents new evidence that RLH waves play a significant role in helicon plasma sources. An experimentally measured plasma density profile in an argon helicon discharge is used to calculate the rf field structure. The calculations are performed using a two–dimensional field solver under the assumption that the density profile is axisymmetric. It is found that RLH waves with an azimuthal wave number *m*=1 form a standing wave structure in the axial direction and that the frequency of the RLH eigenmode is close to the driving frequency of the rf antenna. The calculated resonant power absorption, associated with the RLH eigenmode, accounts for most of the rf power deposited into the plasma in the experiment. *© 2006 American Institute of Physics
*DOI:10.1063/1.2402913

**IFSR-1151**

**Global Energy Confinement Scaling Predictions for Tandem Mirrors**

W. Horton, J. Pratt, H. L. Berk, E. Spencer

Journal of Fusion Energy 5 December 2006: Online

**Abstract**

For an MHD stable system, we investigate the interplay between drift wave (ETG and gyro-Bohm) radial transport and axial losses in the GAMMA-10 experimental facility and the proposed kinetically stabilized tandem mirror (KSTM) fusion reactor. Numerical coefficients in the models are taken to be consistent with tokamak and stellarator databases. The trade off between radial losses and the Pastukhov end losses is examined. We propose the use of a genetic algorithm to optimize the fusion power amplification *Q = P*_{fusion}/*P*_{injected} as a function of the key system parameters. *© 2006 Springer International
*DOI: 10.1007/s10894-006-9059-9

**IFSR-1150**

**Nonlinear control of "fast" light" by "slow" light**

G. Shvets, M. Tushentsov

Journal of Modern Optics 10-20 November 2006, Vol. 53, Nos. 16-17, 2507-2518

**Abstact**

The phenomena of slow and super-luminal propagation of electromagnetic waves are considered in the context of a magnetized plasma with undulator induced transparency (UIT). Without the magnetic undulator, the plasma is opaque to the right-hand circularly polarized radiation at the electron cyclotron frequency. Addition of a helical undulator results in the dramatic slowing down of wave propagation. Super-luminal propagation occurs due to the strong coupling between the right- and left-hand circularly polarized waves. We demonstrate that, depending on the detected wave polarization, super-luminal and slow radiation can be observed at the same frequency. Moreover, the super-luminal signal can be controlled by the intensity of the incident signal. *© 2006 Taylor & Francis
*DOI: 10.1080/09500340600898155

**Exact two-body bound states with Coulomb repulsion in a periodic potential**

S. M. Mahajan, A. Thyagaraja

**Abstract**

It is shown, through an elementary quantum mechanical calculation, that two particles interacting via a short range repulsive force in an external periodic potential can form a bound state. The two-particle wavefunction is labelled by a continuous centre-of-mass momentum. It is bounded and spatially localized in the centre-of-mass system; thus, the spatial wavefunction in the relative distance is square integrable and corresponds to a discrete energy. For instance, a combination of short-range (i.e. screened) binary Coulomb interactions and the periodic potential provided by the stationary ions, can create a two-electron bound state in a crystalline solid (Slater et al 1953 Phys. Rev. 91 1323 and Hubbard 1963 Proc. R. Soc. A 276 238). However, the phenomenon delineated here is universal in the sense that, under appropriate conditions, bound states are possible independent of the nature of the particles and/or the mechanism by which the external periodic potential is engineered. Our general wave mechanical result may explain experimental results presenting evidence of such bound pair states in solids (Gross et al 1971 JETP Lett. 13) and photonic lattices (Winkler et al 2006 Nature 441 853). It has many other potentially interesting consequences even for classical interacting wave systems (e.g. solitons) propagating in a periodic background. This result of wave mechanics and interference is remarkable in that two repulsively interacting particles cannot form a bound state when moving in vacuum. Two non-interacting particles moving in a periodic external potential can only ever form uncorrelated two-particle Bloch states and yet when both physical conditions are present they can move as a 'bound pair'. *© 2006 IOP Publishing Ltd *

DOI: 10.1088/0305-4470/39/47/L01

**Injection, trapping, and acceleration of electrons in a three-dimensional nonlinear laser wakefield **

S. Yu. Kalmykov, L. M. Gorbunov, P. Mora, G. Shvets

**Abstract**

It is demonstrated that the accelerating and focusing phases of the nonlinear three-dimensional axisymmetric laser wake can almost entirely overlap starting from a certain distance behind the laser pulse in homogeneous plasma. Such field structure results from the curvature of phase fronts due to the radially inhomogeneous relativistic shift of plasma frequency. Consequently, the number of trapped low-energy electrons can be much greater than that predicted by the linear wake theory. This effect is favorable for quasimonoenergetic acceleration of a considerable charge (several hundreds of pC) to about 1 GeV per electron in the plasma wakefield driven by an ultrashort (~30 fs) weakly focused (r_{0}~100 µm) petawatt laser pulse. *© 2006 American Institute of Physics *

DOI: 10.1063/1.2363172

**Snapshots of laser wakefields **

N. H. Matlis, S. Reed, S. S. Bulanov, V. Chvykov, G. Kalintchenko, T. Matsuoka, P. Rousseau, V. Yanovsky, A. Maksimchuk, S. Kalmykov, G. Shvets and M. C. Downer

**Abstract**

Tabletop plasma accelerators can now produce GeV-range electron beams^{1-5} and femtosecond X-ray pulses^{6}, providing compact radiation sources for medicine, nuclear engineering, materials science and high-energy physics^{7}. In these accelerators, electrons surf on electric fields exceeding 100 GeV m^{-1}, which is more than 1,000 times stronger than achievable in conventional accelerators. These fields are generated within plasma structures (such as Langmuir waves^{8} or electron density 'bubbles'^{9}) propagating near light speed behind laser^{2-4} or charged-particle^{5} driving pulses. Here, we demonstrate single-shot visualization of laser-wakefield accelerator structures for the first time. Our 'snapshots' capture the evolution of multiple wake periods, detect structure variations as laser–plasma parameters change, and resolve wavefront curvature; features never previously observed. *© Nature Publishing Group*

DOI: 10.1038/nphys442

**Analysis of multifrequency interferometry in a cylindrical plasma **

D. J. Kraft, R. D. Bengtson, B. N. Breizman, D. G. Chavers, C. C. Dobson, J. E. Jones, V. T. Jacobson

**Abstract**

A microwave interferometer operating simultaneously at 70, 90, and 110 GHz is used to measure line integrated electron density in a plasma column in the VX-20 experiment. Interferometer beam sizes are a significant part of the plasma radius at some locations. We model the wave propagation through the plasma using a scalar wave approximation with assumptions of a Gaussian beam profile and plasma spatial profile. The phase shifts obtained from this model are compared with standard thin beam calculations and experimental data. ©* 2006 American Institute of Physics *

DOI: 10.1063/1.2222172

**Alfvén cascades in JET discharges with NBI-heating**

S.E. Sharapov, B. Alper, Yu. F. Baranov, H. L. Berk, D. Borba, C. Boswell, B. N. Breizman, C. D. Challis, M. de Baar, E. De La Luna, E. A. Evangelidis, S. Hacquin, N. C. Hawkes, V. G. Kiptily, S. D. Pinches, P. Sandquist, I. Voitsekhovich, N. P. Young, JET-EFDA Contributors

**Abstact**

Alfvén cascade (AC) eigenmodes excited by energetic ions accelerated with ion-cyclotron resonance heating in JET reversed-shear discharges are studied experimentally in high-density plasmas fuelled by neutral beam injection (NBI) and by deuterium pellets. The recently developed O-mode interferometry technique and Mirnov coils are employed for detecting ACs. The spontaneous improvements in plasma confinement (internal transport barrier (ITB) triggering events) and grand ACs are found to correlate within 0.2 s in JET plasmas with densities up to ~5 × 10^{19} m^{-3}. Measurements with high time resolution show that ITB triggering events happen before 'grand' ACs in the majority of JET discharges, indicating that this improvement in confinement is likely to be associated with the decrease in the density of rational magnetic surfaces just before *q*_{min}(t) passes an integer value. Experimentally observed ACs excited by sub-Alfvénic NBI-produced ions with parallel velocities as low as V_{||NBI} ≈ 0.2 · V_{A} are found to be most likely associated with the geodesic acoustic effect that significantly modifies the shear-Alfvén dispersion relation at low frequency. Experiments were performed with a tritium NBI-blip (short time pulse) into JET plasmas with NBI-driven ACs. Although considerable NBI-driven AC activity was present, good agreement was found both in the radial profile and in the time evolution of DT neutrons between the neutron measurements and the TRANSP code modelling based on the Coulomb collision model, indicating the ACs have at most a small effect on fast particle confinement in this case. © 2006 *IAEA* (www.iop.org/)

DOI:10.1088/0029-5515/46/10/S02

**IFSR-1144**

**Near-Field Microscopy Through a SiC Superlens**

T. Taubner, D. Korobkin, Y. A. Urzhumov, G. Shvets, R. Hillenbrand

Science 15 September 2006: Vol. 313. no. 5793, p. 1595

**Abstract**

The wave nature of light limits the spatial resolution in classical microscopy to about half of the illumination wavelength. Recently, a new approach capable of achieving subwavelength spatial resolution, called superlensing, was invented, challenging the already established method of scanning near-field optical microscopy (SNOM). We combine the advantages of both techniques and demonstrate a novel imaging system where the objects no longer need to be in close proxim-ity to a near-field probe, allowing for optical near-field microscopy of subsurface objects at sub-wavelength-scale lateral resolution. © *Science*

DOI: 10.1126/science.1131025

**Yang-Mills Magnentofluid Unification**

B. A. Bambah, S. M. Mahajan, C. Mukka

**Abstract**

We generalize the hybrid magnetofluid model of a charged fluid interacting with an electromagnetic field to the dynamics of a relativistic hot fluid interacting with a non-Abelian field. The fluid itself is endowed with a non-Abelian charge and the consequences of this generalization are worked out. Applications of this formalism to the quark gluon plasma are suggested. © *2006 The American Physical Society *

DOI: 10.1103/PhysRevLett.97.072301

**On a new fixed point of the renormalization group operator for area-preserving maps**

K. Fuchss, A. Wurm, P. J. Morrison

**Abstract**

The breakup of the shearless invariant torus with winding number ω = √2 - 1 is studied numerically using Greene’s residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and the critical scaling exponents of the torus at breakup are computed. *© 2007 Elsevier*

DOI:10.1016/j.physleta.2007.02.054

**On Heat Loading, Novel Divertors, and Fusion Reactors **

M. Kotschenreuther, P. M. Valanju, S. M. Mahajan

**Abstract**

It is shown that the limited thermal power handling capacity of the standard divertors (used in current, as well as, projected tokamaks) forces extremely high (~95%) radiation fractions ƒ_{Rad} in tokamak fusion reactors [1-3] with heating powers considerably larger than ITER-FEAT [4]. Independent of how the radiation may be apportioned between the scrape off layer (SOL) and the core, these enormous values of ƒ_{Rad} have profound and deleterious consequences on the core confinement and stability to the extent that a high power hypothetical fusion reactor operating with the standard divertor (SD) is not likely to meet the daunting confinement requirements. Even operation in modes that have internal transport barriers (ITBs) [5, 6] is not expected to lead to a dependable fusion power reactor with acceptable economics.

The core confinement and stability problems caused by high ƒ_{Rad} are shown to be adequately addressed by X-Divertors (XD) which, through a flaring of the field lines near the divertor plates, considerably enhance the divertor thermal capacity. The use of this new class of divertors will lower the bar on confinement sufficiently that confinement at the level of the routinely found H-mode [7] could be enough for a fusion reactor. A possible class of experiments that could lay the foundation for an efficient and attractive path to practical fusion power is suggested.

**Coulomb collision operator**

** **
R. D. Hazeltine

**Abstract**

Properties of the Coulomb collision operator that have been found useful in plasma kinetic theory and plasma transport theory are gathered and reviewed, with derivations. The use of velocity-space coordinates appropriate to a magnetized (drift-kinetic) plasma is emphasized. Little of the material is new, although the derivations may be more detailed than is customary.

**Nonlinear evolution of the plasma beat wave: Compressing the laser beat notes via electromagnetic cascading **

S. Yu. Kalmykov, G. Shvets

**Abstract
**

The near-resonant beat wave excitation of an electron plasma wave (EPW) can be employed for generating the trains of few-femtosecond electromagnetic (EM) pulses in rarefied plasmas. The EPW produces a comoving index grating that induces a laser phase modulation at the difference frequency. As a result, the cascade of sidebands red and blue shifted by integer multiples of the beat frequency is generated in the laser spectrum. The bandwidth of the phase-modulated laser is proportional to the product of the plasma length, laser wavelength, and amplitude of the electron density perturbation. When the beat frequency is lower than the electron plasma frequency, the redshifted spectral components are advanced in time with respect to the blueshifted ones near the center of each laser beat note. The group velocity dispersion of plasma compresses so chirped beat notes to a few-laser-cycle duration thus creating a train of sharp EM spikes with the beat periodicity. Depending on the plasma and laser parameters, chirping and compression can be implemented either concurrently in the same, or sequentially in different plasmas. Evolution of the laser beat wave and electron density perturbations is described in time and one spatial dimension in a weakly relativistic approximation. Using the compression effect, we demonstrate that the relativistic bistability regime of the EPW excitation [G. Shvets, Phys. Rev. Lett. **93**, 195004 (2004)] can be achieved with the initially subthreshold beat wave pulse.
© *2006 The American Physical Society *

DOI: 10.1103/PhysRevE.73.046403

**IFSR-1138**

**AEGIS: An adaptive ideal-magnetohydrodynamics shooting code for axisymmetric plasma stability**

L. -J. Zheng, M. Kotschenreuther

JOURNAL OF COMPUTATIONAL PHYSICS 211 (2): 748-766 Jan 20 2006

**Abstract**

A new linear ideal-magnetohydrodynamics stability code for axisymmetric plasmas, AEGIS, is described. The AEGIS code employs adaptive shooting in the radial direction and Fourier decomposition in the poloidal direction. The general solution is a linear combination of the independent solutions of the Euler–Lagrange equations solved by the adaptive shooting. A multiple-region matching technique is used to overcome the numerical difficulty associated with the stiff nature of the independent solutions. Benchmarks with other MHD codes show good agreement. Because it is adaptive, the AEGIS code has very good resolution near the singular surfaces of MHD modes. AEGIS has the additional advantage of allowing the investigation of modes with not only low mode numbers, but also intermediate to high mode numbers. © *2005 Elsevier Inc.*

DOI: 10.1016/j.jcp.2005.06.009

**Acceleration of plasma flows in the closed magnetic fields: Simulation and analysis**

S. M. Mahajan, N. L. Shatashvili, S. V. Mikeladze, K. I. Sigua

**Abstract**

Within the framework of a two-fluid description, possible pathways for the generation of fast flows (dynamical as well as steady) in the closed magnetic fields are established. It is shown that a primary plasma flow (locally sub-Alfvénic) is accelerated while interacting with ambient arcade-like closed field structures. The time scale for creating reasonably fast flows (≳100 km/s) is dictated by the initial ion skin depth, while the amplification of the flow depends on local plasma *β*. It is shown that distances over which the flows become "fast" are ~ 0.01*R*_{0} from the interaction surface (*R*_{0} being a characteristic length of the system); later, the fast flow localizes (with dimensions ≲0.05*R*_{0}) in the upper central region of the original arcade. For fixed initial temperature, the final speed (≳500 km/s) of the accelerated flow and the modification of the field structure are independent of the time duration (lifetime) of the initial flow. In the presence of dissipation, these flows are likely to play a fundamental role in the heating of the finely structured stellar atmospheres; their relevance to the solar wind is also obvious. © *2006 American Institute of Physics*

DOI: 10.1063/1.2204832

**Nonlinearly driven second harmonics of Alfvén cascades **

H. Smith, B. N. Breizman, M. Lisak, D. Anderson

**Abstract**

In recent experiments on Alcator C-Mod [J. A. Snipes et al., Phys. Plasmas **12**, 056102 (2005)], measurements of density fluctuations with phase contrast imaging through the plasma core show a second harmonic of the basic Alfvén cascade (AC) signal. The present paper presents a theory that describes the second-harmonic perturbation as a nonlinear sideband produced by the AC eigenmode via quadratic terms in the magnetohydrodynamic equations. It is shown that in a low-pressure plasma the nonlinear coupling to compressional Alfvén and acoustic perturbations can be neglected when calculating the second-harmonic density. The derived expressions for this density perturbation can potentially be used together with experimental measurements to determine the AC amplitude inside the plasma, rather than just at the edge as with magnetic probes. © *2006 American Institute of Physics*

DOI: 10.1063/1.2192500

**Magnetic plasmon resonance**

A. K. Sarychev, G. Shvets, V. M. Salaev

**Abstract**

It is demonstrated that metallic horseshoe-shaped (also referred to as u-shaped) nanostructures can exhibit a magnetic resonance in the optical spectral range. This magnetic plasmon resonance is distinct from the purely geometric *LC* resonance occurring in perfectly conducting split rings because the plasmonic nature of the metal plays the dominant role. Similarly to the electrical surface plasmon resonance, the magnetic plasmon resonance is determined primarily by the metal properties and nanostructure geometry rather than by the ratio of the wavelength and the structure's size. Magnetic plasmon resonance occurs in nanostructures much smaller in size than the optical wavelength. Electromagnetic properties of periodically assembled horseshoe-shaped nanostructures are investigated, and the close proximity of the electrical and magnetic plasmon resonances is exploited in designing a negative index metamaterial. Close to the magnetic plasmon resonance frequency both magnetic permeability *μ* and electric permittivity *ε * can become negative, paving the way for the development of subwavelength negative index materials in the optical range. © *2006 The American Physical Society *

DOI: 10.1103/PhysRevE.73.036609

**Drift wave instability in the Helimak experiment **

J. C. Perez, W. Horton, K. Gentle, W. L. Rowan, K. Lee, R. B. Dahlburg

**Abstract**

Electrostatic drift wave linear stability analysis is carried out for the Helimak configuration and compared against experimental data. Density fluctuation and cross-spectrum measurements show evidence of a coherent mode propagating perpendicular to the magnetic field which becomes unstable at *k*_{⊥}ρ_{s}~0.15. By comparing the experimental results with the wave characteristic of linear two-fluid theory, this mode is identified as an unstable resistive drift wave driven by the density gradient and magnetic grad-*B*/curvature present in an otherwise magnetohydrodynamic stable steady-state equilibrium. © *2006 American Institute of Physics *

DOI: 10.1063/1.2168401

**IFSR-1133**

**Existence of the Magnetorotational Instability **

S. M. Mahajan, V. Krishnan

**Electrostatic potential fluctuations in a Maxwellian plasma **

R. D. Hazeltine, J. D. Lowrey

**Abstract**

The spatial correlation function of a Maxwellian plasma with perturbations arising in the electrostatic potential due to random ion density fluctuations is examined. The entropy is found from the one-particle distribution function using the Shannon formula and then, using the Einstein method, the probability distribution for the electrostatic potential fluctuation is determined. This straightforward procedure is demonstrated to be a powerful tool in studying plasma correlation functions when the system entropy can be computed. © *2006 American Institute of Physics *

DOI: 10.1063/1.2167585

**Drift-magnetohydrodynamical model of error-field penetration in tokamak plasmas **

A. Cole, R. Fitzpatrick

**Abstract**

A previously published magnetohydrodynamical (MHD) model of error-field penetration in tokamak plasmas is extended to take drift-MHD physics into account. In particular, diamagnetic and semicollisional effects are both fully incorporated into the analysis. The new model is used to examine the scaling of the penetration threshold in ohmic tokamak plasmas.
© *2006 American Institute of Physics *

DOI: 10.1063/1.2178167

**Turbulence induced transport in tokamaks**

I. L. Caldas, F.A. Marcus, A. M. Batista, R. L. Viana, S. R. Lopes, M. V. A. P. Heller, Z. O. Guimar-Filho, P. J. Morrison, W. Horton

**Abstract**

This report is concerned with plasma edge turbulence and its relation to anomalous particle transport in tokamaks. First, experimental evidence of turbulence driven particle transport and measurements of the gradients of the equilibrium profiles in the Brazilian tokamaks TBR and TCABR are presented. Next, diffusion in a two drift-wave system is discussed. In this nonintegrable system, particle transport is associated with the onset of chaotic orbits. Finally, numerical evidence suggesting that a nonlinear three-mode interaction could contribute to the intermittent plasma fluctuations observed in tokamaks is presented.* ©2006 American Institute of Physics*

DOI:10.1063/1.2405962

**Negative index meta-materials based on two-dimensional metallic structures **

G. Shvets, Y. A. Urzhumov

**Abstract**

The electromagnetic properties of two-dimensional metallic nanostructures in the optical frequency range are studied. One example of such a structure is a periodic array of thin metallic strip pairs. The magnetic response of these structures is studied, as is the closely related emergence of the negative index of refraction propagation bands. The presence of such bands is found to critically depend on the proximity of electric and magnetic dipole resonances. It is demonstrated that the frequencies of those resonances are strongly dependent on the ratio of the structure thickness and the plasmonic skin depth. Electromagnetic structures that are much thicker than the plasmonic skin depth are shown to exhibit standard broad antenna resonances at the wavelength roughly twice the strip length. As the structures are scaled down to resonate in the visible/mid-infrared, electrostatic resonances determine the electromagnetic properties of such materials. © *2006 IOP Publishing Ltd.* (http://www.iop.org/)

DOI: 10.1088/1464-4258/8/4/S11

**IFSR-1128**

**Enhanced near-field resolution in midinfrared using metamaterials **

D. Korobkin, Y. A. Urzhumov, G. Shvets

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 23 (3): 468-478 Mar 2006

**Abstract**

We demonstrate that a negative-permittivity material (silicon carbide) sandwiched between two layers of positive-permittivity material (silicon oxide) can be used for enhancement of the resolution of near-field imaging via the superlensing effect. The resulting three-layer metamaterial is also shown to exhibit an enhanced transmission when its effective dielectric permittivity matches that of the vacuum. Experimental far-field diagnostics of the superlensing based on measuring transmission coefficients through the metal-coated superlens is implemented using Fourier-transformed infrared microscopy. Superlensing is shown to be a highly resonant phenomenon manifested in a narrow frequency range. © *2006 Optical Society of America*

**Study of strong cross-field sheared flow with the vorticity probe in the Large Plasma Device**

J. C. Perez, W. Horton, R. D. Bengtson, T. Carter

**Abstract**

This work reports evidence for the existence of coherent structures in steady-state shear-flow driven plasmas in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. **62**, 2875 (1991)] facility at UCLA. The measurements are performed with the vorticity probe (VP), a probe that directly measures the plasma vorticity associated with the **E **×** B** shear flow by means of a method that is both simpler and more accurate than the methods used in neutral fluids. Because the rate of change of vorticity is a key quantity in nonlinear models, as in the Hasegawa-Mima equation, its direct measurement is critical for verification purposes. The physical origin of the rate of change of plasma vorticity from **E **×** B** flow is the divergence of the ion polarization current. Vortex coherent structures occur when the vorticity is a nonlinear function of the stream function. Statistical properties of vorticity are reported and shown to be consistent with the types of coherent structures created by the Kelvin-Helmholtz instability. Comparisons of the measured vortex characteristics with the results from nonlinear simulations of the systems is described. © *2006 American Institute of Physics*

DOI:10.1063/1.2179423

**Global energy confinement scaling predictions for the kinetically stabilized tandem mirror **

J. Pratt, W. Horton

**Abstract**

Transport is studied for the kinetically stabilized tandem mirror, an attractive magnetic confinement device for achieving a steady-state burning plasma. For a magnetohydrodynamic stable system, three different radial transport models with Bohm, gyro-Bohm, and electron temperature gradient (ETG) scaling are derived. As a conservative estimate, numerical coefficients in the models are taken to be consistent with tokamak and stellarator databases. The plug mirrors create an ambipolar potential that controls end losses, whereas radial losses are driven by drift wave turbulence, which lowers the electron temperature through radially trapped particle modes and ETG transport losses. The radial transport equations are analyzed, taking into account the Pastukhov energy and particle end losses. For mirror ratio R_{m}= 9 and a large density ratio between plug and central cell regions, there is a high axial ion confinement potential *Φ / T _{i}* ≫ 1, as demonstrated in the GAMMA-10 by Cho et al. [Nucl. Fusion

DOI: 10.1063/1.2188913

**Nonlinear three-mode interaction and drift-wave turbulence in a tokamak edge plasma **

A. M. Batista, I. L. Caldas, S. R. Lopes, R. L. Viana, W. Horton, P. J. Morrison

**Abstract **

A three-wave interaction model with quadratic nonlinearities and linear growth/decay rates is used to investigate the occurrence of drift-wave turbulence driven by pressure gradients in the edge plasma of a tokamak. Model parameters are taken from a typical set of measurements of the floating electrostatic potential in the tokamak edge region. Some aspects of the temporal dynamics exhibited by the three-wave interaction model are investigated, with special emphasis on a chaotic regime found for a wide range of the wave decay rate. An intermittent transition from periodic to chaotic behavior is observed and some statistical properties, such as the interburst and laminar length interval durations, are explored. © *2006 American Institute of Physics*

DOI: 10.1063/1.2184291