AEGIS-K code for linear kinetic analysis of toroidally axisymmetric plasma stability

L.J. Zheng, M.T. Kotschenreuther, and J.W. Van Dam


A linear kinetic stability code for tokamak plasmas: AEGIS-K (Adaptive EiGenfunction Independent Solutions-Kinetic), is described. The AEGIS-K code is based on the newly developed gyrokinetic theory [L.J. Zheng, M.T. Kotschenreuther, J.W. Van Dam, Phys. Plasmas 14 (2007) 072505]. The success in recovering the ideal magnetohydrodynamics (MHD) from this newly developed gyrokinetic theory in the proper limit leads the AEGIS-K code to be featured by being fully kinetic in essence but hybrid in appearance. The radial adaptive shooting scheme based on the method of the independent solution decomposition in the MHD AEGIS code [L.J. Zheng, M.T. Kotschenreuther, J. Comp. Phys. 211 (2006) 748] is extended to the kinetic calculation. A numerical method is developed to solve the gyrokinetic equation of lowest order for the response to the independent solutions of the electromagnetic perturbations, with the quasineutrality condition taken into account. A transform method is implemented to allow the pre-computed Z-function (i.e., the plasma dispersion function) to be used to reduce the integration dimension in the moment calculation and to assure the numerical accuracy in determining the wave–particle resonance effects. Periodic boundary condition along the whole banana orbit is introduced to treat the trapped particles, in contrast to the usual reflection symmetry conditions at the banana tips. Due to the adaptive feature, the AEGIS-K code is able to resolve the coupling between the kinetic resonances and the shear Alfvén continuum damping. Application of the AEGIS-K code to compute the resistive wall modes in ITER is discussed. © 2010 Elsevier Inc.



Current-interchange tearing modes: Conversion of interchange-type modes to tearing modes

L.J. Zheng and M. Furukawa


It is shown that, in addition to usual neoclassical tearing modes, another type of nonclassical tearing mode exists in tokamaks: viz., current-interchange tearing modes (CITMs). CITMs are directly driven by unstable pressure-driven electromagnetic or electrostatic modes of the interchange type (e.g., interchange/ballooning modes, drift waves, etc.) due to the current gradient in tokamaks. Interchange-type modes exchange not only thermal and magnetic energies between flux tubes but also current. In a plasma with a current (or resistivity) gradient, such an interchange can create a current sheet at a mode resonance surface and result in the excitation of CITMs. Note that the interchange mode (i.e., Rayleigh–Taylor instability) is fundamental to tokamak physics. This new theory has an effect on both resistive magnetohydrodynamic stability and transport theories. Instabilities of the interchange type could be directly converted into CITMs, alternative to forming turbulent eddies through nonlinear coupling as in conventional transport theories. In particular, our CITM theory fills in the component in the transport theory of Rechester and Rosenbluth [Phys. Rev. Lett. 40, 38 (1978)] for the origin of magnetic island structure in axisymmetric tokamaks. © 2010 American Institute of Physics



Generalized two-fluid equilibria: Understanding RT-1 experiments and beyond

Z. Yoshida, S.M. Mahajan, T. Mizushima, Y. Yano, H. Saitoh, and J. Morikawa


Diversity of plasma structures, which degenerates in the ideal magnetohydrodynamic model, can emerge in many ways in a two-fluid plasma endowed with a hierarchy of scales. We study the equilibrium structure of high-beta (high temperature and low-density) electrons in a relatively weak magnetic field. Spontaneous flow generation and strong diamagnetism are clear manifestations of the nonideal two-fluid dynamics scaled, respectively, by the ion and electron-inertia lengths (skin depths). The theory predicts stronger flow and diamagnetism in the nonlinear regime of the two-fluid dynamics. © 2010 American Institute of Physics



Nonlinear dynamics of the electromagnetic ion cyclotron structures in the inner magnetosphere

N.L. Tsintsadze, T.D. Kaladze, J.W. Van Dam, W. Horton, X.R. Fu, and T.W. Garner


Electromagnetic ion cyclotron waves, called EMICs, are widely observed in the inner magnetosphere and can be excited through various plasma mechanisms such as ion temperature anisotropy. These waves interact with magnetospheric particles, which they can scatter into the loss cone. This paper investigates how nonlinearities in the ion fluid equations governing the electromagnetic ion cyclotron waves cause large-amplitude EMIC waves to evolve into coherent nonlinear structures. Both planar soliton structures and also two-dimensional vortex-like nonlinear structures are found to develop out of these nonlinearities. © 2010 The American Geophysical Union



Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

E. Tassi, F.L. Waelbroeck, and D. Grasso


The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guidingcenter density. © 2010 IOP Publishing Ltd



Hamiltonian four-field model for magnetic reconnection: nonlinear dynamics and extension to three dimensions with externally applied fields

E. Tassi, P.J. Morrison, D. Grasso, and F. Pegoraro


The nonlinear dynamics of a two-dimensional (2D) model for collisionless magnetic reconnection is investigated both numerically and analytically. For very low values of the plasma β, parallel magnetic perturbations tend to be proportional to the vorticity perturbations, but as β increases, detachment of these quantities takes place. The subsequent difference between the structure of the vorticity and the parallel magnetic perturbations can be explained naturally in terms of the ‘normal’ field variables that emerge from the noncanonical Hamiltonian theory of the model. A three-dimensional extension of the reconnection model is also presented, its Hamiltonian structure is derived, and the corresponding conservation properties are compared with those of the 2D model. A general method for extending a large class of 2D fluid plasma models to three dimensions, while preserving the Hamiltonian structure, is then presented. Finally, it is shown how such models can also be extended, while preserving the Hamiltonian structure, to include externally applied fields, that can be used, for instance, for modelling resonant magnetic perturbations. © 2010 IAEA, Vienna



Quasi-linear MHD modelling of H-mode plasma response to resonant magnetic perturbations

E. Nardon, P. Tamain, M. Bécoulet, G. Huysmans, and F.L. Waelbroeck


The plasma response to externally imposed resonant magnetic perturbations (RMPs) is investigated through quasi-linear MHD modelling in the case where the resonant surfaces are located in the pedestal of an H-mode plasma. The pedestal is a particular region regarding the question of plasma response to RMPs because of its strong E × B and electron diamagnetic rotations. It is found that a strong rotational screening takes place in most of the pedestal. The RMPs may, however, penetrate in a narrow layer at the very edge, where the plasma is cold and resistive. The possibility that one harmonic of the RMPs may also penetrate if its resonant surface is at a particular location, close to the top of the pedestal, where the E×B and electron diamagnetic rotations compensate each other, is discussed. Finally, the RMPs are found to produce some additional transport, even though they do not penetrate. © 2010 IAEA, Vienna



Formation of coherent vortex streets and transport reduction in electron temperature gradient driven turbulence

M. Nakata, T.-H. Watanabe, H. Sugama, and W. Horton


Vortex structures in slab electron temperature gradient (ETG) driven turbulence are investigated by means of a gyrokinetic simulation with high phase-space resolution. Depending on parameters that determine the eigenfrequency of the linear ETG modes, two different flow structures, i.e., statistically steady turbulence with a weak zonal flow and coherent vortex streets along a strong zonal flow, are observed. The former involves many isolated vortices and their mergers with complicated motion and leads to steady electron heat transport. When the latter is formed, phase difference and high wavenumber components of potential and temperature fluctuations are reduced, and the electron heat transport decreases significantly. It is also found that the phase matching with the potential fluctuation is correlated with the reduction in the imaginary part of the perturbed distribution function, and it occurs not only for the temperature fluctuation but also for any nth velocity moments. A traveling wave solution of a Hasegawa–Mima type equation derived from the gyrokinetic equation with the ETG agrees well with the coherent vortex streets found in the slab ETG turbulence. © 2010 The American Institute of Physics



Integrable maps with non-trivial topology: application to divertor configurations

T. Kroetz, M. Roberto, I.L. Caldas, R.L. Viana, P.J. Morrison, and P. Abbamonte


We explore a method for constructing two-dimensional area-preserving, integrable maps associated with Hamiltonian systems, with a given set of fixed points and given invariant curves. The method is used to find an integrable Poincaré map for the field lines in a large aspect ratio tokamak with a poloidal single-null divertor. The divertor field is a superposition of a magnetohydrodynamic equilibrium with an arbitrarily chosen safety factor profile, with a wire carrying an electric current to create an Χ-point. This integrable map is perturbed by an impulsive perturbation that describes non-axisymmetric magnetic resonances at the plasma edge. The non-integrable perturbed map is applied to study the structure of the open field lines in the scrape-off layer, reproducing the main transport features obtained by integrating numerically the magnetic field line equations, such as the connection lengths and magnetic footprints on the divertor plate. © 2009 IAEA, Vienna



Angular redistribution of nonlinear perturbations: A universal feature of nonuniform flows

W. Horton, J.-H. Kim, G.D. Chagelishvili, J.C. Bowman, and J.G. Lominadze


Classically, the net action of nonlinear turbulent processes is interpreted as either a direct or inverse cascade. However, in nonuniform/shear flows the dominant process is a nonlinear redistribution over wave number angle of perturbation spatial Fourier harmonics. We call this process a nonlinear transverse redistribution (NTR). This phenomenon is demonstrated for a simple two-dimensional constant shear (non-normal) flow by numerically simulating the nonlinear dynamics of coherent and stochastic vortical perturbations in the flow. NTR is a general feature of nonlinear processes that should manifest itself in nonuniform engineering, environmental, and astrophysical flows. The conventional characterization of turbulence in terms of direct and inverse cascades, which ignores NTR, appears to be misleading for shear flow turbulence. We focus on the action of nonlinear processes on the spectral energy. NTR redistributes perturbations over different quadrants of the wave number plane and the interplay of this nonlinear redistribution with linear phenomena becomes intricate: it can realize either positive or negative feedback. In the case of positive feedback, it repopulates the quadrants in wave number space where the shear flow induces linear transient growth. © 2010 The American Physical Society



Laser experiments to simulate coronal mass ejection driven magnetospheres and astrophysical plasma winds on compact magnetized stars

W. Horton, T. Ditmire, and Y.P. Zakharov


Laboratory experiments using a plasma wind generated by laser-target interaction are proposed to investigate the creation of a shock in front of the magnetosphere and the dynamo mechanism for creating plasma currents and voltages. Preliminary experiments are shown where measurements of the electron density gradients surrounding the obstacles are recorded to infer the plasma winds. The proposed experiments are relevant to understanding the electron acceleration mechanisms taking place in shock-driven magnetic dipole confined plasmas surrounding compact magnetized stars and planets. Exploratory experiments have been published [P. Brady, T. Ditmire, W. Horton, et al., Phys. Plasmas 16, 043112 (2009)] with the one Joule Yoga laser and centimeter sized permanent magnets. © 2009 Elsevier B.V.



Plasma Display

R. Hazeltine, M. Porkolab, S. Prager, and R. Stambaugh


Michael Moyer's "Fusion's False Dawn" might give the impression that informed scientists have become skeptical about fusion. This impression is incorrect. Fusion scientists consider their goal to be more tractable and relevant than ever before- and every one of several recently commissioned expert review committees has concurred, concluding that fusion energy should be actively pursued. Magnetic fusion devices have already in 1997 produced 16 million watts of fusion power. The challenges of plasma physics have been sufficiently met that we can confidently design devices that will make copious fusion reactions. ITER is one such device that will enable study of high-energy-gain plasma physics. Fusion researchers worldwide are discussing facilities from specialized experiments to a demonstration power plant to take on our next issues of materials, power extraction and tritium production in a reliable, continuously operating system.© 2010 Scientific American



Research needs workshop for magnetic fusion energy science

R.D. Hazeltine


The process, organization, and results of the Research Needs Workshop for Magnetic Fusion Energy Science are reviewed, and the Workshop Report is briefly surveyed. © 2010 Elsevier B.V.



On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

G.I. Hagstrom and P.J. Morrison


The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, ƒ0(ν), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of ƒ0. We prove that for each ƒ0 there is an arbitrarily small δ 0 in W1,1(ℝ) such that ƒ0 + δ ƒ0 is unstable. When ƒ0 is perturbed by an area preserving rearrangement, ƒ0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in Morrison and Pfirsch (1992) and Morrison (2000). If there is a signature change, then there is a rearrangement of ƒ0 that is unstable and arbitrarily close to ƒ0 with 0 in W.1,1 This result is analogous to Krein’s theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in Cn norm that makes ƒ0 unstable. If ƒ0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it. © 2010 Taylor & Francis Group, LLC



Nonlinear gyrofluid simulations of collisionless reconnection

D. Grasso, E. Tassi, and F.L. Waelbroeck


The Hamiltonian gyrofluid model recently derived by Waelbroeck et al. [Phys. Plasmas 16, 032109 (2009)] is used to investigate nonlinear collisionless reconnection with a strong guide field by means of numerical simulations. Finite ion Larmor radius gives rise to a cascade of the electrostatic potential to scales below both the ion gyroradius and the electron skin depth. This cascade is similar to that observed previously for the density and current in models with cold ions. In addition to density cavities, the cascades create electron beams at scales below the ion gyroradius. The presence of finite ion temperature is seen to modify, inside the magnetic island, the distribution of the velocity fields that advect two Lagrangian invariants of the system. As a consequence, the fine structure in the electron density is confined to a layer surrounding the separatrix. Finite ion Larmor radius effects produce also a different partition between the electron thermal, potential, and kinetic energy, with respect to the cold-ion case. Other aspects of the dynamics such as the reconnection rate and the stability against Kelvin–Helmholtz modes are similar to simulations with finite electron compressibility but cold ions. © 2010 American Institute of Physics



A drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in the pedestals of H-mode tokamak plasmas

R. Fitzpatrick and F.L. Waelbroeck


A drift-magnetohydrodynamical (MHD) fluid model is developed for an isolated, steady-state, helical magnetic island chain, embedded in the pedestal of a large aspect ratio, low-β, circular cross section, H-mode tokamak plasma, to which an externally generated, multiharmonic, static magnetic perturbation whose amplitude is sufficiently large to fully relax the pedestal toroidal ion flow is applied. The model is based on a set of single helicity, reduced, drift- MHD fluid equations which take into account neoclassical poloidal and toroidal flow damping, the perturbed bootstrap current, diamagnetic flows, anomalous cross-field diffusion, average magnetic-field line curvature, and coupling to drift-acoustic waves. These equations are solved analytically in a number of different ordering regimes by means of a systematic expansion in small quantities. For the case of a freely rotating island chain, the main aims of the calculation are to determine the chain’s phase velocity, and the sign and magnitude of the ion polarization term appearing in its Rutherford radial width evolution equation. For the case of a locked island chain, the main aims of the calculation are to determine the sign and magnitude of the polarization term. © 2010 American Institute of Physics



Locked magnetic island chains in toroidally flow damped tokamak plasmas

R. Fitzpatrick and F.L. Waelbroeck


The physics of a locked magnetic island chain maintained in the pedestal of an H-mode tokamak plasma by a static, externally generated, multi-harmonic, helical magnetic perturbation is investigated. The non-resonant harmonics of the external perturbation are assumed to give rise to significant toroidal flow damping in the pedestal, in addition to the naturally occurring poloidal flow damping. Furthermore, the flow damping is assumed to be sufficiently strong to relax the pedestal ion toroidal and poloidal fluid velocities to fixed values determined by neoclassical theory. The resulting neoclassical ion flow causes a helical phase-shift to develop between the locked island chain and the resonant harmonic of the external perturbation. Furthermore, when this phase-shift exceeds a critical value, the chain unlocks from the resonant harmonic and starts to rotate, after which it decays away and is replaced by a helical current sheet. The neoclassical flow also generates an ion polarization current in the vicinity of the island chain which either increases or decreases the chain’s radial width, depending on the direction of the flow. If the polarization effect is stabilizing, and exceeds a critical amplitude, then the helical island equilibrium becomes unstable, and the chain again decays away. The critical amplitude of the resonant harmonic of the external perturbation at which the island chain either unlocks or becomes unstable is calculated as a function of the pedestal ion pressure, the neoclassical poloidal and toroidal ion velocities and the poloidal and toroidal flow damping rates. © 2010 IOP Publishing Ltd



A nonideal error-field response model for strongly shaped tokamak plasmas

R. Fitzpatrick


A model is developed that describes the error-field response of a toroidally rotating tokamak plasma possessing a strongly shaped poloidal cross-section. The response is made up of nondissipative ideal and dissipative nonideal components. The calculation of the ideal response is greatly simplified by employing a large aspect-ratio, constant pressure plasma equilibrium in which the current is entirely concentrated at the boundary. Moreover, the calculation of the resonant component of the nonideal response is simplified by modeling each resonant surface within the plasma as a toroidally rotating, thin resistive shell that only responds to the appropriate resonant component of the perturbed magnetic field. This approach mimics dissipation due to continuum damping at Alfvén and/or sound wave resonances inside the plasma. The nonresonant component of the nonideal response is neglected. The error-fields that maximize the net toroidal locking torque exerted on the plasma are determined via singular value decomposition of the total response matrix. For a strongly dissipative plasma, the locking torque associated with a general error-field is found to peak at a beta value that lies above the no-wall beta-limit, in accordance with experimental observations. © 2010 American Institute of Physics



Magnetic reconnection in weakly collisional highly magnetized electron-ion plasmas

R. Fitzpatrick


A reduced three-field model of two-dimensional magnetic reconnection in a weakly collisional, highly magnetized plasma consisting of isothermal electrons and cold ions is derived from a set of Braginskii-like fluid equations. The model is then used to calculate the linear growth rate of the reconnecting instability in collisionless and semicollisional parameter regimes. © 2010 American Institute of Physics



Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems

C. Chandre, E. Tassi, and P.J. Morrison


We present a Hamiltonian derivation of a class of reduced plasma two-dimensional fluid models, an example being the Charney–Hasegawa–Mima equation. These models are obtained from the same parent Hamiltonian model, which consists of the ion momentum equation coupled to the continuity equation, by imposing dynamical constraints. It is shown that the Poisson bracket associated with these reduced models is the Dirac bracket obtained from the Poisson bracket of the parent model. © 2010 American Institute of Physics




H.L. Berk


Explanation of the JET n = 0 chirping mode H.L. Berk et al 2006 Nucl. Fusion 46 S888-S897

Figure 1(a) was repeated in this article, and the correct figure 1(b) was omitted. Below is figure 1 as it should have been published. © 2010 IAEA



Fast excitation of EGAM by NBI

H.L. Berk and T. Zhou


A new mechanism for the fast excitation of the energetic geodesic acoustic mode (EGAM) is proposed to explain the recent experiment in DIII-D (Nazikian et al 2008 Phys. Rev. Lett. 101 185001), where the mode turns on in less than a millisecond after the turn-on of the neutral beam injection. The existence of loss boundary in pitch angle when beam particles are injected counter to the plasma current is crucial to the formation of negative energy EGAM mode. The resonance of this negative energy wave with energetic particles, whose distribution decreases with energy, destabilizes the mode. We find that when there is a loss region, the onset time of instability can be significantly shorter than it would be if the injected particles had no loss region. © 2010 International Atomic Energy Agency



Transport properties in nontwist area-preserving maps

J.D. Szezech, Jr., I.L. Caldas, S.R. Lopes, R.L. Viana, and P.J. Morrison


Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds. © 2009 American Institute of Physics



MHD equilibrium variational principles with symmetry

T. Andreussi, P.J. Morrison, and F. Pegoraro


The chain rule for functionals is used to reduce the noncanonical Poisson bracket for magnetohydrodynamics (MHD) to one for axisymmetric and translationally symmetric MHD and hydrodynamics. The procedure for obtaining Casimir invariants from noncanonical Poisson brackets is reviewed and then used to obtain the Casimir invariants for the considered symmetrical theories. It is shown why extrema of the energy plus Casimir invariants correspond to equilibria, thereby giving an explanation for the ad hoc variational principles that have existed in plasma physics. Variational principles for general equilibria are obtained in this way. © 2010 IOP Publishing Ltd



Rotational stabilization of resistive wall modes in ITER advanced tokamak scenariosa

L.J. Zheng, M.T. Kotschenreuther, and J.W. Van Dam


Rotational stabilization of n=1 resistive wall modes in ITER advanced scenarios [K. Ikeda, Nucl. Fusion 47 (2007)] is investigated, where n is the toroidal mode number. In particular, we present numerical results for the ITER strongly reversed shear case, in comparison to the weakly reversed shear case. The rotation frequency is assumed to be modestly low. Our investigation employs the adaptive eigenfunction independent solution-kinetic (AEGIS-K) code [L. J. Zheng et al., “AEGIS-K code for linear kinetic analysis of toroidally axisymmetric plasma stability,” J. Comput. Phys. (to be published)], which provides a fully kinetic (nonhybrid) and self-consistent (nonperturbative) description. AEGIS-K includes wave-particle resonances, shear Alfvén continuum damping, trapped particle effects, and parallel electric effects, but not finite Larmor radius effects. In the case without rotation and kinetic effects included, we find that the strongly reversed shear configuration is more favorable for perfectly conducting wall stabilization of resistive wall modes, in that it has a higher conducting wall beta limit than the weakly reversed shear case. With sufficient rotation, the strongly reversed shear case can also achieve a higher beta limit for completely suppressing the resistive wall modes. However, the marginal rotation frequency required for complete resistive wall mode stabilization in the strongly reversed shear case is about twice as high as that required for the weakly reversed shear case. © 2010 American Institute of Physics



Kinetic analysis of the resistive wall modes in the ITER advanced tokamak scenario

L.J. Zheng, M.T. Kotschenreuther, and J.W. Van Dam


It is found that n = 1 resistive wall modes in the ITER advanced scenario can be fully stabilized by modestly low rotation with a rotation frequency (normalized to the Alfvén frequency at the magnetic axis) of about Ω = 0.0075. The existence of this stabilization scheme is proved with the AEGIS-K (Adaptive EiGenfunction Independent Solution-Kinetic) code, which provides a fully kinetic (non-hybrid) and self-consistent (non-perturbative) description
of the system. Wave-particle resonances, shear Alfvén continuum damping, trapped particle effect and the parallel electric effects are all taken into account. The rotation frequency for full stabilization is much larger than the diamagnetic drift frequency; therefore, finite Larmor radius effects are negligible. We also find that the rotation stabilization window opens first near the ideal wall limit. © 2009 International Atomic Energy Agency



Laser-plasma simulations of artificial magnetospher formed by giant coronal mass ejections

Y.P. Zakharov, A.G. Ponomarenko, K.V. Vchivkov, W. Horton, and P. Brady


We employed the laboratory (Laser-Produced Plasmas, LPP) and numerical (3D/PIC-code) simulations to study the resulting state of very strong compression of magnetopause (MP) by CME with effective energy E0 ≥ 1034 ergs directed to the Earth. During probable formation of an Artificial Magnetosphere (AM, in a flow of CME’ plasma around the Earth) with the MP stand-off at Rmp up to (2–3)RE, many catastrophic phenomena could occur in a space and ground networks due to very high curl electric fields induced by world-wide magnetic field’s changes with a SC-rate >50 nT/s. The laboratory models of AM (with Rmp ∼ 0.1–30 cm) were formed around high-field, 1D and 3D magnetic obstacles, overflowing by LPP-blobs with E0 up to kJ and magnetized ions. The shape and internal structure of a large-scale AM were studied at KI-1 facility of the Russian team using a set of B-dot magnetic probes, while the main goal of UT’s small-AM experiment was to explore a possible shock’s generation and relevant electron acceleration. Preliminary results of KI-1 experiments show that the both Rm-size and SC (E0) of AM could be described by modified Chapman-Ferraro Scaling, while the whole SC-distribution (in front “one-half” of equatorial plane)—by well-known “Image Dipole” model of the Earth’s magnetopause field. © 2009 Astrophys Space Sci



Variational coordinate transformation in plasma physics

R.L. White, E.R. Solano, and R.D. Hazeltine


It is well-known from scaling arguments that action-based field theories do not possess localized solutions in spaces of more than one dimension. The same scaling argument, modified to account for external forces, is applied to magnetic plasma confinement in an axisymmetric torus. It yields an integral solvability condition of some interest. © 2009 American Institute of Physics



Symmetry analysis of the Grad-Shafranov equation

R.L. White and R.D. Hazeltine


Lie’s technique of computing symmetries of differential equations is applied to a specific case of the Grad–Shafranov equation. The case considered contains the majority of exact solutions from literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given to allow the reader who is unfamiliar with the subject to use the results given in this paper. Several plots of the level sets or flux surfaces of the new solutions are given. © 2009 American Institute of Physics



Some physical mechanisms of precursors to earthquakes

J.W. Van Dam, W. Horton, N.L. Tsintsadze, T.D. Kaladze, T.W. Garner, and L.V. Tsamalashvili


The existence of precursors to earthquakes at different heights of the earth’s ionosphere is investigated. We analyze a mechanism for the generation of low-frequency large-scale zonal flows by higher frequency, small-scale internal-gravity waves in the electrically neutral troposphere. The nonlinear generation mechanism is based on parametric excitation of convective cells by finite amplitude internal-gravity waves. Measured density perturbations arising due to zonal flow generation may confirm the seismic origin of this mechanism. We also investigate nonlinear propagation of low-frequency seismic-origin internal-gravity perturbations in the stable stratified conductive E-layer. The predicted enhancement of atomic oxygen radiation at wavelength 557.7 nm due to the damping of nonlinear internal-gravity vortices is compared with the observed increase of the night-sky green light intensity before an earthquake. The good agreement suggests that ionospheric internal-gravity vortices can be considered as wave precursors of strong earthquakes. These precursors could be a tool for predicting the occurrence of a massive earthquake or volcano. © 2009 The Japan Society of Plasma Science and Nuclear Fusion Research


Progress towards burning plasma

J.W. Van Dam


The next frontier for fusion science is the study of burning plasmas. The international ITER facility will advance research efforts into this new regime. In this paper we will first define burning plasmas and describe their distinctive features. One such feature is dominant self-heating (exothermic) by a large population of alpha particles, created from thermonuclear reactions. Next, we will briefly review how previous experiments on JET and TFTR to attain breakeven have laid the foundation for taking the present step to ITER. Then, we will describe various physics and technology issues that need to be addressed for burning plasmas. In addition to the scientific opportunities, we will also describe how ITER, being operated as a large-scale international project, is making progress in terms of organization, mission, funding, and programmatic coordination worldwide. © 2009 The Japan Society of Plasma Science and Nuclear Fusion Research



Hamiltonian derivation of the Charney-Hasegawa-Mima equation

E. Tassi, C. Chandre, and P.J. Morrison


The Charney–Hasegawa–Mima equation is an infinite-dimensional Hamiltonian system with dynamics generated by a noncanonical Poisson bracket. Here a first principle Hamiltonian derivation of this system, beginning with the ion fluid dynamics and its known Hamiltonian form, is given. © 2009 American Institute of Physics



Stability and nonlinear dynamics aspects of a model for collisionless magnetic reconnection

E. Tassi, D. Grasso, F. Pegoraro, and P.J. Morrison


A Hamiltonian 4-field fluid model describing magnetic reconnection in collisionless plasmas is investigated both analytically and numerically. The noncanonical Hamiltonian structure of the model is used in order to derive equilibrium equations and sufficient conditions for stability of equilibria in the presence of toroidal flow. Numerical simulations of the model equations are then used in order to investigate the vorticity evolution in the nonlinear regime. The coexistence of vortex-sheet-like and filamented structures is observed, which had no counterpart in a previously investigated 2-field model. Such evolution of the vorticity field is explained using the Casimir functionals of the system. Comments on the dependence of the vorticity structure on the value of the electron skin depth are also given. © 2009 The Japan Society of Plasma Science and Nuclear Fusion Research


Spectrum of global magnetorotational instability in a narrow transition layer

J. Pino and S.M. Mahajan


The global magnetorotational instability is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstablemode is of the same order or smaller than the width of this region, the growth rates can differ significantly from those given by a local analysis. In addition, the nonaxisymmetric spectrum admits overstable modes with a nontrivial dependence on azimuthal wavelength, a feature missed by the local theory. In the limit of vanishing transition region width, the Rayleigh-centrifugal instability is recovered in the axisymmetric case, and the Kelvin–Helmholtz instability in the nonaxisymmetric case. © 2009 The American Astronomical Society



Thoughts on brackets and dissipation: old and new

P.J. Morrison


Bracket formulations of two kinds of dynamical systems, called incomplete and complete, are reviewed and developed, including double bracket and metriplectic dynamics. Dissipation based on the Cartan-Killing metric is introduced. Various examples of incomplete and complete dynamics are discussed, including dynamics associated with three-dimensional Lie algebras. © 2009 IOP Publishing Ltd



Linear superposition of nonlinear waves

S.M. Mahajan and H. Miura


Exact nonlinear (arbitrary amplitude) wave-like solutions of an incompressible, magnetized, non-dissipative two-fluid system are found. It is shown that, in1-D propagation, these fully nonlinear solutions display a rare property; they can be linearly superposed. © 2008 Cambridge University Press



Destabilizing Effect of Dynamical Friction on Fast-Particle-Driven Waves in a Near-Threshold Nonlinear Regime

M.K. Lilley, B.N. Breizman, and S.E. Sharapov


The nonlinear evolution of waves excited by the resonant interaction with energetic particles, just above the instability threshold, is shown to depend on the type of relaxation process that restores the unstable distribution function. When dynamical friction dominates over diffusion in the phase space region surrounding the wave-particle resonance, an explosive evolution of the wave is found to be the only solution. This is in contrast with the case of dominant diffusion when the wave may exhibit steady-state, amplitude modulation, chaotic and explosive regimes near marginal stability. The experimentally observed differences between Alfve´nic instabilities driven by neutral beam injection and those driven by ion-cyclotron resonance heating are interpreted. © 2009 The American Physical Society



Plasma transport and turbulence in the Helimak: Simulation and experiment

B. Li, B.N. Rogers, P. Ricci, and K.W. Gentle


The Helimak experiment produces a toroidal plasma with a helical magnetic field. A simulation-experiment comparison of turbulence in this device is presented, focusing on parameter regimes in which the turbulence is dominated by interchange modes with k≃0. The numerical simulations are based on a two-dimensional electrostatic two-fluid model that evolves the full radial profiles of plasma density, the electric potential, and the electron temperature. The simulation results are compared with the experiment and general agreement is found for the plasma profiles, the autocorrelation functions, the frequency spectra, the cross-correlation functions, and the probability density functions. Some quantitative differences between the simulation and experimental data are
also discussed. © 2009 American Institute of Physics



Fluid models of impurity transport via drift wave turbulence

S. Futatani, W. Horton, S. Benkadda, I.O. Bespamyatnov, and W.L. Rowan


Turbulent transport due to drift waves is a critical issue for fusion physics across all magnetic confinement geometries. Three-component fluid equations are used to find the eigenmodes and eigenfrequencies of a nonuniform, magnetized plasma with a four dimensional fluctuation vector composed of fluctuations of the electron density, the working gas ion density, the impurity density, and the electrostatic plasma potential. This structure of the eigenmodes and eigenvectors is shown for two collisionality regimes: (i) the collisional drift waves appropriate for the scrape-off-layer and the edge plasma in limiter discharges and (ii) the trapped electron mode taken in the limit of a Terry–Horton fluid description for the core plasma. From the eigenmodes and eigenvectors the part of the density and potential fluctuations that are out-of-phase is computed. The quasilinear particle fluxes are analyzed as a function of the power spectrum of the plasma potential fluctuations and the gradient parameters characterizing the Ohmic, H, and internal transport barrier confinement modes. A reversal in a direction of impurity flux is observed by changing the sign of the impurity density gradient length. After reversal, the impurity flux is directed outward and it is a favorable for fusion plasmas. © 2010 American Institute of Physics



A numerical matching technique for linear resistive magnetohydrodynamics modes

M. Furukawa, S. Tokuda, and L.J. Zheng


A new numerical matching technique for linear stability analysis of resistive magnetohydrodynamics (MHD) modes is developed. The solution to the resistive reduced MHD equations in an inner layer with a finite width is matched onto the solution to the inertialess ideal MHD or the Newcomb equation by imposing smooth disappearance of parallel electric field in addition to the continuity of perturbed magnetic field and its spatial gradient. The boundary
condition for the parallel electric field is expressed as a boundary condition of the third kind for the stream function of the perturbed velocity field. This technique can be applied for the reversed magnetic shear plasmas of their minimum safety factors being rational numbers, for which the conventional asymptotic matching technique fails. In addition, this technique resolves practical difficulties in applying the conventional asymptotic matching technique, i.e., the sensitivity of the outer-region solution on the accuracy of the local equilibrium as well as the grid arrangements, even in normal magnetic shear plasmas. Successful applications are presented not only for the eigenvalue problem but also for the initial-value problem. © 2010 American Institute of Physics



Effect of local E×B flow shear on the stability of magnetic islands in tokamak plasmas

R. Fitzpatrick and F.L. Waelbroeck


The influence of local E×B flow shear on a relatively wide, constant-ψ, magnetic island embedded in a large-aspect-ratio, low-β, circular cross-section tokamak plasma is examined, using a slab approximation to model the magnetic geometry. It is found that there are three separate solution branches characterized by low, intermediate, and high values of the shear. Flow shear is found to have a stabilizing effect on island solutions lying on the low and high shear branches, via a nonlinear modification of the ion polarization term in the Rutherford island width evolution equation, but to have a destabilizing effect on solutions lying on the intermediate shear branch. Moreover, the effect is independent of the sign of the shear. The modification of island stability by local E×B flow shear is found to peak when the magnitude of the shear is approximately vi /Ls, where vi is the ion thermal velocity, and Ls the magnetic shear length. © 2009 American Institute of Physics



Comment on ‘Magnetic topology effects on Alcator C-Mod scrape-off layer flow’

A.Y. Aydemir


In their recent paper [1] Simakov et al (hereafter referred to as the authors) draw attention to certain differences between their work and mine [2] and claim that my results contradict an earlier work by Cohen and Ryutov [3] while theirs are in agreement, thus questioning the validity of my work. The authors are wrong in their assertion. My work is correct and in agreement with the relevant portions of Cohen and Ryutov’s. There are, however, serious errors in the two primary authors’ earlier work [4] and its erratum [5] (the erratum itself is in error) on which this paper [1] is based. © 2009 IOP Publishing Ltd



Generation of Fast Ions by Microclusters

Alexey Arefiev, Boris Breizman, Vladimir Khudik, Xiaohui Gao, and Michael Downer


Laser-irradiated microclusters can generate energetic ions that produce fusion reactions. The amount and spectrum of these ions depend on the cluster-size distribution, electron heating mechanism, and cluster expansion dynamics. This paper describes recent physics results pertinent to the items listed. It is shown that the size distribution of large clusters can be determined from absorption measurements in a pump-probe experiment. It is also shown how a laser can create a two-component electron distribution with a hot minority whose energies exceed the ponderomotive potential. The heating rate and the limitations on electron energy are examined. The hot electron component expands with an equal number of ions. A first-principle model is presented that describes ion acceleration by the hot electron pressure together with adiabatic cooling of the hot electrons. © 2010 The Japan Society of Plasma Science and Nuclear Fusion Research



Relaxed states in relativistic multifluid plasmas

Jesse Pino, Hui Li, and Swadesh Mahajan


The evolution equations for a plasma comprising multiple species of charged fluids with relativistic bulk and thermal motion are derived. It is shown that a minimal fluid coupling model allows a natural casting of the evolution equations in terms of generalized vorticity, which treats the fluid motion and electromagnetic fields equally. Equilibria can be found using a variational principle based on minimizing the total enstrophy subject to energy and helicity constraints. A subset of these equilibria corresponds to minimum energy. The equations for these states are presented with example solutions showing the structure of the relaxed states. © 2010 American Institute of Physics



Effect of dynamical friction on nonlinear energetic particle modes

M. K. Lilley, B. N. Breizman, and S. E. Sharapov


A fully nonlinear model is developed for the bump-on-tail instability including the effects of dynamical friction (drag) and velocity space diffusion on the energetic particles driving the wave. The results show that drag provides a destabilizing effect on the nonlinear evolution of waves. Specifically, in the early nonlinear phase of the instability, the drag facilitates the explosive scenario of the wave evolution, leading to the creation of phase space holes and clumps that move away from the original eigenfrequency. Later in time, the electric field associated with a hole is found to be enhanced by the drag, whereas for a clump it is reduced. This leads to an asymmetry of the frequency evolution between holes and clumps. The combined effect of drag and diffusion produces a diverse range of nonlinear behaviors including hooked frequency chirping, undulating, and steady state regimes. An analytical model is presented, which explains the aforementioned diversity. A continuous production of hole-clump pairs in the absence of collisions is also observed. © 2010 American Institute of Physics



Parameter Optimization Studies for a Tandem Mirror Neutron

W. Horton, X. R. Fu, A. Ivanov, and A. Beklemishev


A basic plasma physics tandem mirror experiment is proposed to develop the potential uses of magnetic mirror confined plasmas for a neutron source. We consider parameter variations from the currently operating symmetric mirror plasma trap GDT in an attempt to optimize the neutron source intensity while minimizing the expense and complications of the system. The combined radial and axial plasma loss rates are analyzed and shown to yield an optimal operational point that minimizes the required auxiliary heating power. © Springer Science+Business Media, LLC 2010



Twisting Space-Time: Relativistic Origin of Seed Magnetic Field and Vorticity

S. M. Mahajan, and Z. Toshida


We demonstrate that a purely ideal mechanism, originating in the space-time distortion caused by the demands of special relativity, can break the topological constraint (leading to helicity conservation) that would forbid the emergence of a magnetic field (a generalized vorticity) in an ideal nonrelativistic dynamics. The new mechanism, arising from the interaction between the inhomogeneous flow fields and inhomogeneous entropy, is universal and can provide a finite seed even for mildly relativistic flows.



The super X divertor (SXD) and a compact fusion neutron source (CFNS)

M. Kotschenreuther, P. Valanju, S. Mahajan, L. J. Zheng, L. D. Pearlstein, R. H. Bulmer, J. Canik, and R. Maingi


A new magnetic geometry, the superXdivertor (SXD), is invented to solve severe heat exhaust problems in high power density fusion plasmas. SXD divertor plates are moved to the largest major radii inside the TF coils, increasing the wetted area by 2–3 and the line length by 2–5. Two-dimensional fluid simulations with SOLPS (Schneider et al 2006 SOLPS 2-D edge calculation code Contrib. Plasma Phys. 46) show a several-fold decrease in divertor heat flux and plasma temperature at the plate. A small high power density tokamak using SXD is proposed, for either (1) useful fusion applications using conservative physics, such as a component test facility (CTF) or fission– fusion hybrid, or (2) to develop more advanced physics modes for a pure fusion reactor in an integrated fusion environment. © 2010 IAEA, Vienna, IOP Publishing Ltd.



Nonlinear travelling waves in energetic particle phase space

B. N. Breizman


An exact nonlinear solution is found for long-time behaviour of spontaneously formed phase space clumps/holes in dissipative plasmas with a population of energetic particles. This solution represents a Bernstein–Greene–Kruskal mode with slowly varying shape and velocity. It describes a continuous transformation of a plasma eigenmode excited just above the instability threshold into an energetic particle mode with a significantly different frequency. An electrostatic bump-on-tail instability is chosen to illustrate the analysis. However, generality of the resonant particle dynamics makes the described approach applicable to other resonance-dominated instabilities, including rapid frequency-sweeping events for Alfvénic modes in tokamaks. © 2010 IOP Publishing Ltd.



Nonlinear magnetohydrodynamic effects on Alfvén eigenmode evolution and zonal flow generation

Y. Todo, H. L. Berk and B. N. Beizman


Nonlinear magnetohydrodynamic (MHD) effects on Alfvén eigenmode evolution were investigated via hybrid simulations of an MHD fluid interacting with energetic particles. The investigation focused on the evolution of an n = 4 toroidal Alfvén eigenmode (TAE) which is destabilized by energetic particles in a tokamak. In addition to fully nonlinear code, a linear-MHD code was used for comparison. The only nonlinearity in that linear code is from the energetic-particle dynamics. No significant difference was found in the results of the two codes for low saturation levels, δB/B ∼ 10−3. In contrast, when the TAE saturation level predicted by the linear code is δB/B ∼ 10−2, the saturation amplitude in the fully nonlinear simulation was reduced by a factor of 2 due to the generation of zonal (n = 0) and higher-n (n  ≥  8) modes. This reduction is attributed to the increased dissipation arising from the nonlinearly generated modes. The fully nonlinear simulations also show that geodesic acoustic mode is excited by the MHD nonlinearity after the TAE mode saturation.© 2010 IOP Publishing Ltd.



Energetic-Particle-Driven Instabilities in General Toroidal Configurations

D. A. Spong, B. N. Breizman, D. L. Brower, E. D'Azevedo, C. B. Deng, A. Konies, Y. Todo, and K. Toi


Energetic-particle driven instabilities have been extensively observed in both tokamaks and stellarators. In order for such devices to ultimately succeed as D-T fusion reactors, the super-Alfvénic 3.5 Mev fusion-produced alpha particles must be sufficiently well confined. This requires the evaluation of losses from classical collisional transport processes as well as from energetic particle-driven instabilities. An important group of instabilities in this context are the discrete shear Alfvén modes, which can readily be destabilized by energetic particles (with velocities of the order of vAlfvén) through wave-particle resonances. While these modes in three-dimensional systems have many similarities to those in tokamaks, the detailed implementation of modeling tools has required development of new methods. Recent efforts in this direction will be described here, with an emphasis on reduced models. © 2010 WILEY-VCH VerlagGmbH & Co. KGaA, Weinheim



Relativistic Petschek reconnection with pressure anisotropy in a pair-plasma

J. M. TenBarge, R. D. Hazeltine and S. M. Mahajan


Reconnection of magnetic field lines for a wide range of parameters in the relativistic regime is considered. A newly developed covariant fluid model for magnetized plasmas, incorporating pressure anisotropy, is used to expand the study of the petschek-type reconnection in a pair-plasma governed by slow-mode shocks. The plasma parameters are found to be strongly modified by anisotropy on both sides of the shock. © 2010 The Authors. Journal compilation © 2010 RAS



Stable optical vortex solitons in pair plasmas

V. I. Berezhiani, S. M. Mahajan, and N. L. Shatashvili


It is shown that the pair plasmas with small temperature asymmetry can support existence of localized as well as delocalized optical vortex solitons. Coexistence of such solitons is possible due to peculiar form of saturating nonlinearity which has a focusing-defocusing nature—for weak amplitudes being focusing becoming defocusing for higher amplitudes. It is shown that delocalized vortex soliton is stable in entire region of its existence while single- and multicharged localized vortex solitons are unstable for low amplitudes and become stable for relativistic amplitudes. © The American Physical Society.

DOI: 10.1103/PhysRevA.81.053812


Application of Double Beltrami states to solar eruptions

D. Kagan and S. M. Mahajan


We show that the general class of Double Beltrami (DB) states, which are the lowest energy equilibria of Hall magnetohydrodynamics, can have characteristics similar to those of active regions in the solar corona and is capable of undergoing a catastrophe that can cause a solar eruption, such as a flare or coronal mass ejection (CME). We then show that the qualitative evolution of the DB state is consistent with that of a solar eruption. Finally, we make two quantitative comparisons ofDBstates to CMEs,which are the simplest result of the catastrophe. First, we show that the DB expansion by a factor of 1–2 before the catastrophe is consistent with the increase in the height of the leading edges of Large-Angle Spectrometric Coronagraph (LASCO C1) CMEs in the quasi-equilibrium stage. Secondly, we use the assumption that DB states are randomly chosen from the allowed phase space of coronal structures to predict that the probability of a coronal structure erupting is 0.046. Identifying active regions with DB states and using observational constraints to estimate that the state is replaced every 60min by emerging loops results in a CME rate of 11 d−1, which is in reasonable agreement with the actual rate of about 6 d−1 at solar maximum. © 2010 The Authors. Journal compilation © 2010 RAS



Two-fluid temperature-dependent relativistic waves in magnetized streaming pair plasmas

A. R. Soto-Chavez, S. M. Mahajan, and R. D. Hazeltine


A relativistic two-fluid temperature-dependent approach for a streaming magnetized pair plasma is considered. Such a scenario corresponds to secondary plasmas created at the polar caps of pulsar magnetospheres. In the model the generalized vorticity rather than the magnetic field is frozen into the fluid. For parallel propagation four transverse modes are found. Two are electromagnetic plasma modes which at high temperature become light waves. The remaining two are Alfvénic modes split into a fast and slow mode. The slow mode is cyclotron two-stream unstable at large wavelengths and is always subluminous. We find that the instability cannot be suppressed by temperature effects in the limit of large (finite) magnetic field. The fast Alfvén mode can be superluminous only at large wavelengths, however it is always subluminous at high temperatures. In this incompressible approximation only the ordinary mode is present for perpendicular propagation. For oblique propagation the dispersion relation is studied for finite and large strong magnetic fields and the results are qualitatively described. © The American Physical Society.



Stable localized electromagnetic pulses in asymmetric pair plasmas

V. I. Berezhiani, S. M. Mahajan, and N. L. Shatashvili


It is shown that pair plasmas, through the new focusing-defocusing non-linearity generated by an "asymmetry" in initial temperatures of constituent species, can support multidimensional, stable, large-amplitude light bullets as well as bullets carrying vortices, i.e., spinning bullets © 2010 Cambridge University Press.


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