Behavior of n = 1 magnetohydrodynamic modes of infernal type at high-mode pedestal with plasma rotation

L.J. Zheng, M.T. Kotschenreuther and P. Valanju


Magnetohydrodynamic instabilities of high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation for stability. The jointed European torus-like equilibria of H-mode discharges are generated numerically using the VMEC code. It is found that, when the bootstrap current is taken into account, a safety-factor reversal or plateau can be generated near plasma edge. This confirms previous results of numerical equilibrium reconstructions using other types of codes. The n = 1 magnetohydrodynamic instabilities, where n is toroidal mode number, are investigated numerically in this type of equilibria using the AEGIS code. It is found that the infernal type harmonic can prevail at safety-factor reversal or plateau region. The toroidal plasma rotation effect with low Mach number is investigated. The numerical results show that the mode frequency is close to the rotation frequency at pedestal top, when the value of safety factor at plateau is slightly above a rational number. This mode frequency range seems to coincide with the experimentally observed frequencies of n = 1 edge harmonic oscillations (or outer modes) at the quiescent H-mode discharges. © 2013 American Institute of Physics



Generating vorticity and magnetic fields in plasmas in general relativity: Spacetime curvature drive

F.A. Asenjo, S.M. Mahajan and A. Qadir


Using the generally covariant magnetofluid formalism for a hot plasma, a spacetime curvature driven mechanism for generating seed vorticity/magnetic field is presented. The “battery” owes its origin to the interaction between the gravity modified Lorentz factor of the fluid element and the inhomogeneous plasma thermodynamics. The general relativistic drive is evaluated for two simple cases: seed formation in a simplified model of a hot plasma accreting in stable orbits around a Schwarzschild black hole and for particles in free fall near the horizon. Some astrophysical applications are suggested. © 2013 American Institute of Physics



Local thermodynamics of a magnetized, anisotropic plasma

R.D. Hazeltine, S.M. Mahajan and P.J. Morrison


An expression for the internal energy of a fluid element in a weakly coupled, magnetized, anisotropic plasma is derived from first principles. The result is a function of entropy, particle density and magnetic field, and as such plays the role of a thermodynamic potential: it determines in principle all thermodynamic properties of the fluid element. In particular it provides equations of state for the magnetized plasma. The derivation uses familiar fluid equations, a few elements of kinetic theory, the MHD version of Faraday’s law, and certain familiar stability and regularity conditions. © 2013 American Institute of Physics



Pfirsch-Schlüter current-driven edge electric frields and their effect on the L-H transition power threshold

A.Y. Aydemir


An important contribution to the magnetohydrodynamic equilibrium at the tokamak edge comes from the Pfirsch–Schlüter current. The parallel electric field that can be associated with these currents is necessarily poloidally asymmetric and makes a similarly nonuniform contribution to the radial electric field on a flux surface. Here the role of the poloidal variation of this radial electric field in the L–H transition power threshold is investigated. Dependence of the resulting electric fields on magnetic topology, geometric factors such as the upper/lower triangularity and elongation, and the relative position of the X-point(s) in the poloidal plane are examined in detail. Starting with the assumption that an initially more negative radial electric field at the edge helps lower the transition power threshold, we find that our results are in agreement with a variety of experimental observations. In particular, for a 'normal’ configuration of the plasma current and toroidal field we show the following. (i) The net radial electric field contribution by the Pfirsch–Schlüter currents at the plasma edge is negative for a lower single null and positive for a corresponding upper single null geometry. (ii) It becomes more negative as the X- point height is reduced. (iii) It also becomes more negative as the X-point radius is increased. These observations are consistent with the observed changes in the L–H transition power threshold PLH under similar changes in the experimental conditions. In addition we find that (iv) in USN with an unfavourable ion ∇B drift direction, the net radial electric field contribution is positive but decreases as the X-point radius decreases. This is consistent with the C-Mod observation that an L–I mode transition can be triggered by increasing the upper triangularity in this configuration. (v) Locally the radial electric field is positive above the outer mid-plane and reverses sign with reversal of the toroidal field, consistent with DIII-D observations in low-power L-mode discharges. Thus, taken as a whole, the Pfirsch–Schlüter current-driven fields can explain a number of observations on the L–H or L–I transition and the required power threshold PLH levels not captured by simple scaling laws. They may indeed be an important ‘hidden variable’. © 2012 IAEA, Vienna



Special issue containing papers presented at the 12th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems (7-11 September 2011)

H.L. Berk


The topic of the behaviour of energetic alpha particles in magnetic fusion confined plasmas is perhaps the ultimate frontier plasma physics issue that needs to be understood in the quest to achieve controlled power from the fusion reaction in magnetically confined plasmas. The partial pressure of alpha particles in a burning plasma will be ∼5–10% of the total pressure and under these conditions the alpha particles may be prone to develop instability through Alfvénic interaction. This may lead, even with moderate alpha particle loss, to a burn quench or severe wall damage. Alternatively, benign Alfvénic signals may allow the vital information to control a fusion burn. © 2012 IAEA, Vienna



Spin-Gradient-Driven Light Amplification in an Quantum Plasma

S. Braun, F.A. Asenjo, and S.M. Mahajan


It is shown that the gradient ‘‘free-energy’’ contained in equilibrium spin vorticity can cause electromagnetic modes, in particular the light wave, to go unstable in a spin quantum plasma of mobile electrons embedded in a neutralizing ion background. For densities characteristic of both the solid state and very high density astrophysical systems, the growth rates are sufficiently high to overcome the expected collisional damping. Preliminary results suggest a powerful spin-inhomogeneity driven mechanism for stimulating light amplification. © 2012 American Physical Society



Shearless transport barriers in magnetically confinded plasmas

I.L. Caldas, R.L. Viana, C.V. Abud, J.C.D. Fonseca, Z.O. Guimarães Filho, T. Kroetz, F.A. Marcus, A.B. Schelin, J.D. Szezech Jr., D.L. Toufen, S. Benkadda, S.R. Lopes, P.J. Morrison, M. Roberto, K. Gentle, Y. Kuznetsov and I.C. Nascimento


Shearless transport barriers appear in confined plasmas due to non-monotonic radial profiles and cause localized reduction of transport even after they have been broken. In this paper we summarize our recent theoretical and experimental research on shearless transport barriers in plasmas confined in toroidal devices. In particular, we discuss shearless barriers in Lagrangian magnetic field line transport caused by non-monotonic safety factor profiles. We also discuss evidence of particle transport barriers found in the TCABR Tokamak (University of São Paulo) and the Texas Helimak (University of Texas at Austin) in biased discharges with non-monotonic plasma flows. © 2012 IOP Publishing Ltd



Spontaneous healing and growth of locked magnetic island chains in toroidal plasmas

R. Fitzpatrick and F.L. Waelbroeck


Recent experiments have demonstrated that locked magnetic island chains in stellarator plasmas spontaneously heal under certain conditions, and spontaneously grow under others. A formalism initially developed to study magnetic island dynamics in tokamak plasmas is employed to investigate this phenomenon. It is found that island healing/growth transitions can be caused either by a breakdown in torque balance in the vicinity of the island chain, or by an imbalance between the various terms in the island width evolution equation. The scaling of the healing/growth thresholds with the standard dimensionless plasma parameters β, ν*, and ρ* is determined. In accordance with the experimental data, it is found that island healing generally occurs at high β and low ν*, and island growth at low β and high ν*. In further agreement, it is found that island healing is accompanied an ion poloidal velocity shift in the electron diamagnetic direction, and island growth by a velocity shift in the ion diamagnetic direction. Finally, it is found that there is considerable hysteresis in the healing/growth cycle, as is also seen experimentally. © 2012 American Institute of Physics



Nonlinear error-field penetration in low density ohmically heated tokamak plasmas

R. Fitzpatrick


A theory is developed to predict the error-field penetration threshold in low density, ohmically heated, tokamak plasmas. The novel feature of the theory is that the response of the plasma in the vicinity of the resonant surface to the applied error-field is calculated from nonlinear drift-MHD (magnetohydrodynamical) magnetic island theory, rather than linear layer theory. Error-field penetration, and subsequent locked mode formation, is triggered once the destabilizing effect of the resonant harmonic of the error-field overcomes the stabilizing effect of the ion polarization current (caused by the propagation of the error-field-induced island chain in the local ion fluid frame). The predicted scaling of the error-field penetration threshold with engineering parameters is (br/BT)crit ∼ ne B −1.8 T R −0.25 0 , where br is the resonant harmonic of the vacuum radial error-field at the resonant surface, BT the toroidal magnetic field-strength, ne the electron number density at the resonant surface and R0 the major radius of the plasma. This scaling—in particular, the linear dependence of the threshold with density—is consistent with experimental observations. When the scaling is used to extrapolate from JET to ITER, the predicted ITER error-field penetration threshold is (br/BT)crit ∼ 5 × 10−5, which just lies within the expected capabilities of the ITER error-field correction system. © 2013 American Institute of Physics



1.5D quasilinear model and its application on beams interacting with Alfvén eigenmodes in DIII-D

K. Ghantous, N.N. Gorelenkov, W.W. Heidbrink, and M.A. Van Zeeland


We propose a model, denoted here by 1.5D, to study energetic particle (EP) interaction with toroidal Alfvenic eigenmodes (TAE) in the case where the local EP drive for TAE exceeds the stability limit. Based on quasilinear theory, the proposed 1.5D model assumes that the particles diffuse in phase space, flattening the pressure profile until its gradient reaches a critical value where the modes stabilize. Using local theories and NOVA-K simulations of TAE damping and growth rates, the 1.5D model calculates the critical gradient and reconstructs the relaxed EP pressure profile. Local theory is improved from previous study by including more sophisticated damping and drive mechanisms such as the numerical computation of the effect of the EP finite orbit width on the growth rate. The 1.5D model is applied on the well-diagnosed DIII-D discharges #142111 [M. A. Van Zeeland et al., Phys. Plasmas 18, 135001 (2011)] and #127112 [W. W. Heidbrink et al., Nucl. Fusion. 48, 084001 (2008)]. We achieved a very satisfactory agreement with the experimental results on the EP pressure profiles redistribution and measured losses. This agreement of the 1.5D model with experimental results allows the use of this code as a guide for ITER plasma operation where it is desired to have no more than 5% loss of fusion alpha particles as limited by the design. © 2012 American Physics



Magnetic island evolution in hot ion plasmas

A. Ishizawa, F.L. Waelbroeck, R. Fitzpatrick, W. Horton, and N. Nakajima


Effects of finite ion temperature on magnetic island evolution are studied by means of numerical simulations of a reduced set of two-fluid equations which include ion as well as electron diamagnetism in slab geometry. The polarization current is found to be almost an order of magnitude larger in hot than in cold ion plasmas, due to the strong shear of ion velocity around the separatrix of the magnetic islands. As a function of the island width, the propagation speed decreases from the electron drift velocity (for islands thinner than the Larmor radius) to values close to the guiding-center velocity (for islands of order 10 times the Larmor radius). In the latter regime, the polarization current is destabilizing (i.e., it drives magnetic island growth). This is in contrast to cold ion plasmas, where the polarization current is generally found to have a healing effect on freely propagating magnetic island. © 2012 American Physics



Magnetic phase transitions in plasmas and transport barriers

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


A model of magnetic phase transitions in plasmas is presented: plasma elements with pressure excess or defect are dia- or paramagnets and move radially under the influence of the background plasma magnetization. It is found that magnetic phase separation could be the underlying mechanism of L to H transitions and drive transport barrier formation. Magnetic phase separation and the associated pedestal build-up, as described here, can be explained by the well-known interchange mechanism, now reinterpreted as a magnetization interchange. The interchange mechanism can drive motion of plasma elements even when stable. A testable necessary criterion for the L to H transition is presented. © 2012 IAEA, Vienna



Effective transport barriers in nontwist systems

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


In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents. © 2012 American Physical Society



Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands

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


This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ≥ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping. © 2012 IAEA, Vienna



Undamped electrostatic plasma waves

F. Valentini, D. Perrone, F. Califano, F. Pegoraro, P. Veltri, P.J. Morrison, and T.M. O'Neil


Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named corner modes. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the (k, ωR) plane (ωR being the real part of the wave frequency and k the wavenumber), away from the well-known “thumb curve” for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower k-values and chopping the tail shifts them toward higher k- values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas. © 2012 American Institute of Physics



Role of singular layers in the plasma response to resonant magnetic perturbations

F.L. Waelbroeck, I. Joseph, E. Nardon, M. Bécoulet, and R. Fitzpatrick


The response of an H-mode plasma to magnetic perturbations that are resonant in the edge is evaluated using a fluid model. With two exceptions, the plasma rotation suppresses the formation of magnetic islands, holding their widths to less than a tenth of those predicted by the vacuum approximation. The two exceptions are at the foot of the pedestal, where the plasma becomes more resistive, and at the surface where the perpendicular component of the electron velocity reverses. The perturbations exert a force on the plasma so as to brake the perpendicular component of the electron rotation. In the pedestal, the corresponding Maxwell stress drives the radial electric field in such a way as to accelerate ion rotation. Despite the suppression of the islands, the perturbations give rise to particle fluxes caused by magnetic flutter, with a negligible contribution from E × B convection. In the pedestal, the fluxes are such as to reduce the density. © 2012 IAEA, Vienna



Influence of rotating resonant magnetic perturbation on the plasma radial electric field on TEXTOR

T. Zhang, Y. Liang, Y. Sun, A. Krämer-Flecken, S. Soldatov, E. Nardon, P. Tamain, F.L. Waelbroeck, Y. Yang, J. Pearson, H.R. Koslowski, and the TEXTOR team


The plasma radial electric field (Er ) has been changed by applying an n = 1 counter-rotating resonant magnetic perturbation (RMP) field with a frequency of 5 kHz in ohmic plasmas on TEXTOR. The change in the ErEr) is negative, different from the observations in previous experiments where ΔEr was always positive when a static or low frequency (∼1 kHz) rotating RMP field was applied in the plasma on TEXTOR. The Er profile in the present experiment shows two distinct evolution stages. In the first stage, ΔEr from the q = 2 to q = 3 surfaces have a similar decrease as the amplitude of the 5 kHz counter-rotating field increases. In the second stage, the decrease rate of ΔEr is faster for the positions closer to the q = 2 surface. As a result, the Er around the q = 2 surface has a significant change in this second stage while no change of Er is observed near the q = 3 surface even after the excitation of an m/n = 2/1 tearing mode. A reduced MHD code, 4FC, has been used to model the experiment. Two simulations have been performed. The first one is by applying a single 2/1 perturbation while both, 2/1 and 3/1 perturbations, have been applied in the second simulation. The result from the second simulation is qualitatively consistent with the experimental observations while the first simulation including only a single 2/1 perturbation cannot explain the evolution of the Er profile in the second stage as observed in the experiment. © 2012 IAEA, Vienna



Simulation and theory of spontaneous TAE frequency sweeping

G. Wang, and H.L. Berk


A simulation model, based on the linear tip model of Rosenbluth, Berk and Van Dam (RBV), is developed to study frequency sweeping of toroidal Alfvén eigenmodes (TAEs). The time response of the background wave in the RBV model is given by a Volterra integral equation. This model captures the properties of TAE waves both in the gap and in the continuum. The simulation shows that phase space structures form spontaneously at frequencies close to the linearly predicted frequency, due to resonant particle–wave interactions and background dissipation. The frequency sweeping signals are found to chirp towards the upper and lower continua. However, the chirping signals penetrate only the lower continuum, whereupon the frequency chirps and mode amplitude increases in synchronism to produce an explosive solution. An adiabatic theory describing the evolution of a chirping signal is developed which replicates the chirping dynamics of the simulation in the lower continuum. This theory predicts that a decaying chirping signal will terminate at the upper continuum though in the numerical simulation the hole disintegrates before the upper continuum is reached. © 2012 American Physical Society



Ballooning theory of the second kind-two dimensional tokamak modes

T. Xie, Y.Z. Zhang, S.M. Mahajan, and A.K. Wang


The 2-D ballooning transform, devised to study local high toroidal number (n) fluctuations in axisymmetric toroidal system (like tokamaks), yields a well- defined partial differential equation for the linear eigenmodes. In this paper, such a ballooning equation of the second kind is set up for ion temperature gradient driven modes pertinent to a 2-D non-dissipative fluid plasma; the resulting partial differential equation is numerically solved, to calculate the global eigenvalues, and the 2-D mode structure is presented graphically along with analytical companions. The radial localization of the mode results from translational symmetry breaking for growing modes and is a vivid manifestation of spontaneous symmetry breaking in tokamak physics. The eigenmode, poloidally ballooned at ϑ = ±π/2, is radially shifted from associated rational surface. The global eigenvalue is found to be very close to the value obtained in 1-D parameterized (λ = ∓π/2) case. The 2-D eigenmode theory is applied to estimate the toroidal seed Reynolds stress [Y. Z. Zhang, Nucl. Fusion Plasma Phys. 30, 193 (2010)]. The solution obtained from the relatively simplified ballooning theory is compared to the solution of the basic equation in original coordinate system (evaluated via FFTs); the agreement is rather good. © 2012 American Institute of Physics



Free boundary ballooning mode representation

L.J. Zheng


A new type of ballooning mode invariance is found in this paper. Application of this invariance is shown to be able to reduce the two-dimensional problem of free boundary high n modes, such as the peeling-ballooning modes, to a one-dimensional problem. Here, n is toroidal mode number. In contrast to the conventional ballooning representation, which requires the translational invariance of the Fourier components of the perturbations, the new invariance reflects that the independent solutions of the high n mode equations are translationally invariant from one radial interval surrounding a single singular surface to the other intervals. The conventional ballooning mode invariance breaks down at the vicinity of plasma edge, since the Fourier components with rational surfaces in vacuum region are completely different from those with rational surfaces in plasma region. But, the new type of invariance remains valid. This overcomes the limitation of the conventional ballooning mode representation for studying free boundary modes. © 2012 American Institute of Physics



Self-organized confinement by magnetic dipole: recent results from RT-1 and theoretical modeling

Z. Yoshida, H. Saitoh, Y. Yano, H. Mikami, N. Kasaoka, W. Sakamoto, J. Morikawa, M. Furukawa, and S.M. Mahajan


Inhomogeneous magnetic field gives rise to interesting properties of plasmas which are degenerate in homogeneous (or zero) magnetic fields. Magnetospheric plasmas, as observed commonly in the Universe, are the most simple, natural realization of strongly inhomogeneous structures created spontaneously in the vicinity of magnetic dipoles. The RT-1 device produces a ‘laboratory magnetosphere’ by which stable confinement (particle and energy confinement times ∼0.5 s) of high-β (local electron β ∼ 0.7; electron temperature ≳10 keV) plasma is achieved. By producing a pure-electron plasma, we obtain clear-cut evidence of inward (or up-hill) diffusion of particles. A statistical mechanical model reveals the ‘distortion’ of phase space, induced by the inhomogeneity of the ambient magnetic field, on which the plasma relaxes into an equilibrium with inhomogeneous density while it maximizes the entropy. © 2013 IOP Publishing Ltd



Gap eigenmode of radially localized helicon waves in a periodic structure

L. Chang, B.N. Breizman, and M.J. Hole


An ElectroMagnetic Solver (Chen et al 2006 Phys. Plasmas 13 123507) is employed to model a spectral gap and a gap eigenmode in a periodic structure in the whistler frequency range. A radially localized helicon mode (Breizman and Arefiev 2000 Phys. Rev. Lett. 84 3863) is considered. We demonstrate that the computed gap frequency and gap width agree well with a theoretical analysis, and find a discrete eigenmode inside the gap by introducing a defect to the system’s periodicity. The axial wavelength of the gap eigenmode is close to twice the system’s periodicity, which is consistent with Bragg’s law. Such an eigenmode could be excited by energetic electrons, similar to the excitation of toroidal Alfvén eigenmodes by energetic ions in tokamaks. Experimental identification of this mode is conceivable on the large plasma device (Gekelman et al 1991 Rev. Sci. Instrum. 62 2875). © 2013 IOP Publishing Ltd



On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets

C. Chandre, L. de Guillebon, A. Back, E. Tassi, and P.J. Morrison


The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional derivatives. The role of these projectors is investigated by using Dirac’s theory of constrained Hamiltonian systems. Results are illustrated by three examples taken from plasma physics: magnetohydrodynamics, the Vlasov–Maxwell system, and the linear two-species Vlasov system with quasineutrality. © 2013 IOP Publishing Ltd



Finite-time rotation number: A fast indicator for chaotic dynamical structures

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


Lagrangian coherent structures are effective barriers, sticky regions, that separate chaotic phase space regions of different dynamical behavior. The usual way to detect such structures is by calculating finitetime Lyapunov exponents. We show that similar results can be obtained for time-periodic systems by calculating finite-time rotation numbers, which are faster to compute. We illustrate our claim by considering examples of continuous- and discrete-time dynamical systems of physical interest. © 2012 Elsevier B.V.



Neutron spin quantum plasmas - Ferromagnetism as a related state

S.M. Mahajan, and F.A. Asenjo


It is shown that a ferromagnetic “minimum energy relaxed state” is accessible to a neutron fluid. We model the neutron fluid as a spin quantum plasma where the electromagnetic interaction is trough the magnetic moment of the neutron. The neutron ferromagnetism results from the macroscopic spin alignment that occurs due to a profound interplay between the classical and spin quantum vorticities carried by the charge-less neutron fluid. The simplest manifestation of a neutron superfluidity comes about by an exact cancellation of the quantum and classical vorticities to create a helicity free system. © 2013 Elsevier B.V.



Deformation of vortex patches by boundaries

A. Crosby, E.R. Johnson, and P.J. Morrison


The deformation of two-dimensional vortex patches in the vicinity of fluid boundaries is investigated. The presence of a boundary causes an initially circular patch of uniform vorticity to deform. Sufficiently far away from the boundary, the deformed shape is well approximated by an ellipse. This leading order elliptical deformation is investigated via the elliptic moment model of Melander, Zabusky, and Styczek [J. Fluid Mech. 167, 95 (1986)]. When the boundary is straight, the centre of the elliptic patch remains at a constant distance from the boundary, and the motion is integrable. Furthermore, since the straining flow acting on the patch is constant in time, the problem is that of an elliptic vortex patch in constant strain, which was analysed by Kida [J. Phys. Soc. Jpn. 50, 3517 (1981)]. For more complicated boundary shapes, such as a square corner, the motion is no longer integrable. Instead, there is an adiabatic invariant for the motion. This adiabatic invariant arises due to the separation in times scales between the relatively rapid time scale associated with the rotation of the patch and the slower time scale associated with the selfadvection of the patch along the boundary. The interaction of a vortex patch with a circular island is also considered. Without a background flow, the conservation of angular impulse implies that the motion is again integrable. The addition of an irrotational flow past the island can drive the patch towards the boundary, leading to the possibility of large deformations and breakup. © 2013 American Institute of Physics.



Influence of wall thickness on the stability of the resistive wall mode in tokamak plasmas

R. Fitzpatrick


The influence of finite wall thickness on the stability of the resistive wall mode (RWM) in a tokamak is determined using a simple cylindrical plasma model in which the dissipation required to stabilize the mode is provided by neoclassical parallel ion viscosity. For present-day tokamaks, which possess relatively thin walls, finite wall thickness effects are found to have relatively little influence on the RWM stability boundaries, which are almost the same as those calculated in the thin-wall limit. On the other hand, for next-step devices, which are likely to possess much thicker walls than present-day tokamaks, finite wall thickness effects are found to significantly impede the ability of plasma rotation to stabilize the RWM all the way to the perfect-wall stability limit. © 2013 American Institute of Physics



Stability of compressible reduced magnetohydrodynamic equilibria—Analogy with magnetorotational instability

P.J. Morrison, E. Tassi, and N. Tronko


Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical δW criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of δW is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instability (MRI) for the latter model corresponds to the condition for interchange instability in CRMHD, with the Coriolis term and shear velocity playing the roles of the curvature term and pressure gradient, respectively. Using the EC method, stability conditions for the rotating disk model, for a large class of equilibria with possible non-uniform magnetic fields, are obtained. In particular, this shows it is possible for the MRI system to undergo, in addition to the MRI, another instability that is analogous to the kink instability. For vanishing magnetic field, the Rayleigh hydrodynamical stability condition is recovered. © 2013 AIP Publishing LLC



A general theory for gauge-free lifting

P.J. Morrison


A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physics, the particle dynamics replaces conventional constitutive relations for matter. Several examples are considered including the usual Vlasov-Maxwell theory, a guiding center kinetic theory, Vlasov-Maxwell theory with the inclusion of spin, and a Vlasov-Maxwell theory with the inclusion of Dirac’s magnetic monopoles. All are shown to be Hamiltonian field theories and the Jacobi identity is proven directly. © 2013 American Institute of Physics



Vortex bubble formation in pair plasmas

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


It is shown that delocalized vortex solitons in relativistic pair plasmas with small temperature asymmetries can be unstable for intermediate intensities of the background electromagnetic field. Instability leads to the generation of ever-expanding cavitating bubbles in which the electromagnetic fields are zero. The existence of such electromagnetic bubbles is demonstrated by qualitative arguments based on a hydrodynamic analogy, and by numerical solutions of the appropriate nonlinear Schrödinger equation with a saturating nonlinearity. © 2013 American Physical Society



Spatio-temporal profiling of cluster mass fraction in a pulsed supersonic gas jet by frequency-domain holography

X. Gao, A.V. Arefiev, R.C. Korzekwa, X. Wang, B. Shim, and M.C. Downer


We present an in-depth study of a rapid, noninvasive, single-shot optical method of determining cluster mass fraction ƒc(r, t) at specified positions r within, and at time t after opening the valve of, a pulsed high-pressure pulsed supersonic gas jet. A ~2 mJ, 40 fs pump pulse ionizes the monomers, causing an immediate drop in the jet’s refractive index njet proportional to monomer density, while simultaneously initiating hydrodynamic expansion of the clusters. The latter leads to a second drop in njet that is proportional to cluster density and is delayed by ~1 ps. A temporally stretched probe pulse measures the 2-step index evolution in a single shot by frequency-domain holography, enabling recovery of ƒc. We present a model for recovering ƒc from fs-time-resolved phase shifts. We also present extensive measurements of spatio-temporal profiles ƒc(r, t) of cluster mass fraction in a high-pressure supersonic argon jet for various values of backing pressure P0 and reservoir temperature T0. © 2013 AIP Publishing LLC



Energetic Particle Instabilities in Fusion Plasmas

S.E. Sharapov, B. Alper, H.L. Berk, D.N. Borba, B.N. Breizman, C.D. Challis, I.G.J. Classen, E.M. Edlund, J. Erickson, A. Fasoli, E.D. Fredrickson, G.Y. Fu, M. Garcia-Munoz, T. Gassner, K. Ghantous, V. Goloborodko, N.N. Gorelenkov, M.P. Gryanznevich, S.Hacquin, W.W. Heidbrink, C. Hellesen, V.G. Kiptily, G.J. Kramer, P. Lauber, M.K. Lilley, M. Lisak, F. Nabais, R. Nazikian, R. Nyqvist, M. Osakabe, C. Perez von Thun, S.D. Pinches, M. Podesta, M. Porkolab, K. Shinohara, K. Schoepf, Y. Todo, K. Toi, M.A. Van Zeeland, I. Voitsekhovich, R.B. White, V. Yavorskij, ITPA EP TG, and JET-EFDA Contributors


Remarkable progress has been made in diagnosing energetic particle instabilities on present-day machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfvén instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge.


Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

M. Kotschenreuther, P. Valanju, B. Covele, and S. Mahajan


Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes. © 2013 AIP Publishing LLC



Observation of Self-Sustaining Relativistic Ionization Wave Launched by a Sheath Field

M. McCormick, A.V. Arefiev, H.J. Quevedo, R.D. Bengtson, and T. Ditmire


We present experimental evidence supported by simulations of a relativistic ionization wave launched into a surrounding gas by the sheath field of a plasma filament with high energy electrons. Such a filament is created by irradiating a clustering gas jet with a short pulse laser (115 fs) at a peak intensity of 5 × 1017 W=cm2. We observe an ionization wave propagating radially through the gas for about 2 ps at 0.2–0.5 c after the laser has passed, doubling the initial radius of the filament. The gas is ionized by the sheath field, while the longevity of the wave is explained by a moving field structure that traps the high energy electrons near the boundary, maintaining a strong sheath field despite the significant expansion of the plasma. © 2014 American Physical Society



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