Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration


 Charlotte Booth
 1 years ago
 Views:
Transcription
1 Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration D.A. Kaltsas and G.N. Throumoulopoulos Department of Physics, University of Ioannina, GR Ioannina, Greece s: Abstract A Solovevlike solution describing equilibria with field aligned incompressible flows [Throumoulopoulos and Tasso, Phys. Plasmas 19, (01)] is extended to non parallel flows. The solution expressed as a superposition of Bessel functions contains an arbitrary number of free parameters which are exploited to construct a variety of configurations including ITER shaped ones. For parallel flows application of a sufficient condition for linear stability shows that this condition is satisfied in an appreciable part of the plasma region on the highfield side mostly due to the variation of the magnetic field perpendicular to the magnetic surfaces. Also, the results indicate that depending on the shape of the Machfunction profile and the values of the free parameters the flow and flow shear may have either stabilizing or destabilizing effects. 1
2 The most known and widely employed axisymmetric magnetohydrodynamic analytic equilibrium is associated with the Solovév solution of the GradSfafranov (GS) equation [1]. However, this solution being updown symmetric and having a limited number of free parameters can not describe configurations with diverted shaping of contemporary tokamaks. This drawback was eliminated in Refs. [, 3] by introducing an arbitrary number of additional terms in the homogeneous part of the solution by means of an iterative technique. Consequently, by exploiting the respective arbitrary number of free parameters a variety of equilibria with desirable shaping and confinement figures of merit were constructed. Since sheared flows play a role in the transitions to improved confinement regimes as the LH transition, in a previous study [4] we extended this solution to confined plasmas with incompressible flows parallel to the magnetic field. Also, we considered the linear stability of the extended solution by means of a sufficient condition [5]. Aim of the present contribution is to extend further this Solovévlike solution to plasmas with incompressible flows of arbitrary direction on the basis of a generalized GS equation [Eq. (1) below]. Unlike the usual form of the Solovév solution we employ a separable solution of the homogeneous part of the generalized GS equation expressed in terms of Bessel functions. Thus, alternative to Refs. [, 3, 4] an arbitrary number of free parameters is introduced through a linear combination of these functions. For parallel flows we reexamine the stability by applying the condition of Ref. [5] and compare the results with those of Ref. [4]. We employ the generalised GS [6, 7] u + 1 ( d X du 1 Mp ) + µ 0 R dp s du + µ R 4 0 d [ ϱ(φ ) ] = 0 (1) du in conjunction with the Bernoulli equation for the pressure [ v ( ) ] dφ P = P s ϱ ρ du () Here (R, ϕ, z) are cylindrical coordinates with z corresponding to the axis of symmetry; the function u = u(r, z) related to the poloidal magnetic flux labels the magnetic surfaces; M p (u) is the poloidal Alfvén Mach function and ϱ(u) the massdensity function being a surface quantity because of incompressibility; X(u) relates to the toroidal magnetic field, P s (u) is the static pressure and Φ(u) the electrostatic potential; ( the elliptic operator in (1) is defined as = R 1 ) R R R + z. The negative velocity term in () sets an upper limit on the flow amplitude, v, so that the relation P 0 is satisfied everywhere in the plasma. However, the positive term ϱρ (dφ/du) permits higher flow amplitudes in comparison with field aligned flows (dφ/du = 0). Derivation of (1) and () is given in [6] and [7]. For convenience we introduce the dimensionless quantities ρ = R/R 0, ζ = z/r 0, ũ = u/(b 0 R0), ϱ = ϱ/ϱ 0, P = P/(B 0 /µ 0 ), J = J/ (B 0 /µ 0 R 0 ), ṽ = v/ ( B 0 / ) µ 0 ϱ 0, where R0 is the major radius of the torus and B 0 the vacuum magnetic field at the geometric centre. Eq. (1) then remains identical in form with µ 0 set formally equal to one. In the following analysis the tildes will be dropped on the understanding that we refer to dimensionless quantities. The terms X /(1 Mp ), P s and ϱ ( ) dφ du being free surface functions can be chosen arbitrarily. We adopt a Solovevlike linearizing Ansatz: X (u) 1 M p [ dφ(u) = X0 + X 1 u, P s (u) = P 0 + P 1 u, ϱ du where X 0, X 1, P 0, P 1, G 0, G 1 are free parameters. Then Eq. (1) assumes the form ] = G 0 + G 1 u (3) u ρ 1 u ρ ρ + u ζ + X 1 + P 1 ρ + G 1 ρ 4 = 0 (4) As already mentioned in the first paragraph of this study we construct a solution of the homogeneous part of Eq. (4) with arbitrary number of free parameters. Unlike previous papers [, 3, 4], in which
3 such solutions were produced by using an iterative algorithm, here a homogeneous separable solution is expressed in terms of Bessel functions restricting the separation constant to integer values by exploiting the orthogonality of these functions. The homogeneous solution is: u h (ρ, ζ) = cρ j [ aj J 1 (jρ)e jζ + b j J 1 (jρ)e jζ + c j Y 1 (jρ)e jζ + d j Y 1 (jρ)e jζ] (5) where J 1 and Y 1 are the first order Bessel functions of first and second kind respectively and j is the separation constant. A particular solution of (4) can be obtained by inspection as and therefore the general solution is written u p (ρ, ζ) = P 1 8 ρ4 G 1 4 ρ6 X 1 ζ (6) u = u h + u p (7) It is noted that (7) holds for arbitrary Mach functions M p and densities ϱ. The coefficients a j, b j, c j, d j (j = 1,..., 3) can be specified in connection with the desirable boundary shaping and the parameters P 1, G 1, X 1 in connection with the desirable values of the various physical quantities, e.g, for large tokamaks the pressure, current density and electric field are on the order of 10 6 P a, 10 6 A/m and 10 4 V/m respectively. The parameter c can be fixed by the condition q a = 1.1 (so that the KruskalShafranov stability criterion is satisfied) where q a is the safety factor on axis: q a = I ρ 1 Mp ( u ) 1/ u ρ ζ (8) ρ=ρa,ζ=ζa with I the poloidal current function I = (1 Mp ) X 1/ 0 + X 1u + ρ M p G 0 + G 1u (9) To completely construct the equilibrium we adopt a peaked offaxis choice for the poloidal Mach function: M p = M a ( ) m ( ) n mua nua u n (u a u) m (10) m + n m + n where u a refers to the magnetic axis and M a is the maximum value of M p. Typical values of M p for large tokamaks are of order of 10 4 according to the experimental scaling v 10 1 v s, where v s = (γp/ϱ) 1/ is the sound velocity. The parameters m and n are chosen in such a way that the flow be localised near the boundary in connection with the LH transition phenomenology. Also we choose a linear density function: ϱ = ϱ a u/u a. Once all the arbitrary functions are specified we can construct singlenull diverted equilibria, e.g., ITER like ones, by imposing appropriate boundary conditions. For the boundary shaping we follow the method of Refs. [], [4]. We impose the shaping conditions at four prescribed characteristic points of the boundary (inner, outer, upper and lower): (1 ε, 0), (1 + ε, 0), (1 δε, κε), (1 δε, κε), where a is the minor radius of the torus, δ is the triangularity, κ the elongation and ε = a/r 0 the inverse aspect ratio. For the ITER machine the respective planned values are a = m, δ = 0.33, κ = 1.33 and the major radius of the torus is R 0 = 6. m. The conditions are: u(1 ε, 0) = u(1 + ε, 0) = u(1 δε, κε) = u(1 δε, κε) = 0 (11) u ρ (1 δε, κε) = 0 (1) u ζ (1 ε, 0) = u ζ (1 + ε, 0) = 0 (13)
4 u ζ (1 δε, κε) = u ρ (1 δε, κε) = 0 (14) (1 α) u ζζ (1 ε, 0) + εκ u ρ (1 ε, 0) = 0 (15) (1 + α) u ζζ (1 + ε, 0) εκ u ρ (1 + ε, 0) = 0 (16) κ u ρρ (1 δε, κε) ε cos α u ζ(1 δε, κε) = 0 (17) where α = arcsin δ. Conditions (11) impose u to vanish at the four characteristic points, (1) ensures the local symmetry of the boundary curve at the upper point, while (13) relates to local updown symmetry near the plane z = 0. Conditions (14) produce the xpoint topology of the lower point and relations (15), (16), (17) (which are proved in Ref. [4]) are related to the curvature of the boundary curve at the inner, outer and upper point respectively. On account of the above system of 1 equations we truncate the summation in expression (5) so as to include the first 1 terms. The constants a i, b i, c i, d i (i = 1,..., 3) are determined by numerically solving the set of Eqs. (1117). As an example, an ITERlike equilibrium is given in Fig. 1. Also we constructed Dshaped and Doublenull diverted configurations by making the Ζ Fig. 1: An ITERlike equilibrium with flow of arbitrary direction in connection with solution (7). The basic geometrical parameters are a = m, δ = 0.33, κ = 1.33, R 0 = 6. m. proper changes in the shaping conditions regarding the upper and lower points. The equilibria have safety factor profiles increasing monotonically from the magnetic axis to the plasma boundary, current density profiles increasing throughout the plasma from the inner to the outer point in connection with the ansatz (3) (Fig. ), electric fields localized in the flow region and possessing an extremum, and peaked pressure profiles vanishing on the boundary by adjusting the free parameter P 0 (Fig. 3). An interesting result is that the flow creates local pressure extrema (Fig. 3) associated with the formation of pressure islands shown in Fig 4. Also, sufficiently large flows can create paramagnetic current layers. Such an example is shown in Fig. 5. We now consider the linear stability of the equilibria constructed for field aligned flows by applying the sufficient condition of Ref. [5]. This condition states that a stationary equilibrium with field aligned incompressible flow and constant mass density is stable to small three dimensional perturbations if M p < 1 and A 0 where A = A 1 + A + A 3 + A 4 (18) A 1 = (J u) (19)
5 J φ,0 A m Fig. : Toroidal current density profile on the plane ζ = 0 increasing from the inner to the outer point. The local extrema are formed in the toroidal layer where the flow takes place P,0 Pa Fig. 3: Pressure profile on the plane ζ = 0. In the regions where the flow is located the profile has local extrema in accordance with Bernoulli s law.
6 Fig. 4: Isobaric surfaces with flow created pressure islands around the local extrema of Fig J Ζ,0 A m Fig.5 The ζ component of the current density. Owing to the flow a paramagnetic current layer of J ζ is formed. A = (J u) ( u )B (0) A 3 = 1 4 (1 M p ) 1 dm p du u u B (1) A 4 = 1 (1 M p ) 3/ dm p du u 4 g () ( 1 dp g = s 1 Mp du dm ) p B (3) du The quantity A 1 being always negative consists a destabilizing contribution potentially related to current driven modes. The other terms can be either stabilizing or destabilizing. Specifically, the term A relates to the current density and the variation of the magnetic field perpendicular to the magnetic surfaces. The term A 3 involves the shear and magnitude of the flow in conjunction with the variation of the magnitude of the magnetic field perpendicular to the magnetic surfaces. A 4 is mostly a flow term depending on the magnitude and the shear of the flow. The flows satisfying (1) are inherently subalfvénic (M p < 1) because of an integral transformation involved [7]. For parallel flows the equilibrium is obtained from the solution (5)(7) with G 1 = 0. Also, M p is the Alfvén Mach function of the parallel velocity because in this case it can be shown that the poloidal Mach function, the respective toroidal Mach function and
7 Ζ Ζ Fig. 6: Stability diagrams for the quantity A for the Mach function (10) and two different values of M a: M a = 10 (left) and M a = 4 10 (right). In the red (gray) coloured regions the stability condition is satisfied. The stability area slightly shrinks as M a takes larger values. the (total) parallel Mach function are equal one another. In this paragraph in addition to the localized peakedoffaxis Mach function (10) we adopted the extended peakedonaxis Mach function: ( ) l u (4) M p = M a u a where the parameter l is associated with the flow shear. The quantity A was calculated analytically. After a broad variation of the values of the free parameters (in particular we permitted M p to vary up to the order of 10 1, close to the nonnegativepressure limit) we came to the following conclusions: 1. The condition A 0 is satisfied in a part of the plasma region on the high field side (Figs. 67) where the current density, J, is sufficiently small so that the term A can overcome A 1. Unlike, such a stable region was not found for the equilibria of [4] corresponding to the same ansatz (3) for the free functions (with vanishing nonparallelflow term). The reason should be the different homogeneous solution constructed here. Since J is an increasing function of ρ the non positive term A 1 dominates over the other terms for sufficiently large values of ρ. Therefore the current density J plays a destabilizing role in connection with the negative term A 1.. In the majority of the cases considered the term A related to the magnetic shear is stabilizing. 3. Depending on the shape of the Mach function and the parametric values, the flow and flow shear can have either destabilizing or stabilizing effects. An example in the former case is given in Fig. 6 and another in the latter case in Fig. 7. We have constructed analytically a Solovevlike equilibrium solution with arbitrary number of free parameters by means of a superposition of Bessel functions which can be assigned in connection with desirable boundary shaping. Hence using appropriate sets of boundary conditions we derived a variety of configurations including single null diverted, ITERlike ones. For parallel flows application of a sufficient condition for linear stability implies that this condition is satisfied in an appreciable part of the plasma on the high field side restricted however for large distances from the axis of symmetry by respective large current densities. The magnetic shear in general plays a stabilizing role while the flow and flow shear can be either stabilizing or destabilizing.
8 Ζ Ζ Fig. 7: Stability diagrams for the quantity A for the Mach function (4) with l = and M a = 4 (left), M a = 0.5 (right). The red (gray) coloured region in which the stability condition is satisfied broadens as M a increases. One of the authors (GNT) would like to thank Henri Tasso, George Poulipoulis and Apostolos Kuiroukidis for very useful discussions. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the by (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme under grant agreement No The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] L. S. Solovév, Sov. Phys.JETP 6, 400 (1968). [] A. J. Cerfon and J. P. Freidberg, Phys. Plasmas 17, 0350 (010). [3] R. Srinivarsan, L. L. Lao and M. S. Chu, Plasma Phys. Controlled Fusion 5, (010). [4] G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 19, (01). [5] G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 14, 1104 (007). [6] H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 5, 378 (1998). [7] C. Simintzis, G. N. Throumoulopoulos, G. Pantis, and H. Tasso, Phys. Plasmas 8, 641 (001).
arxiv: v2 [physics.plasmph] 30 Aug 2016
Exact solutions of the GradShafranov equation via similarity reduction and applications to magnetically confined plasmas Dimitrios A. Kaltsas, George N. Throumoulopoulos Department of Physics, University
More informationarxiv: v1 [physics.plasmph] 1 Mar 2016
1 Axisymmetric equilibria with pressure anisotropy and plasma flow A. Evangelias 1,a), G. N. Throumoulopoulos 1,a) 1 University of Ioannina, Physics Department, arxiv:1603.00445v1 [physics.plasmph] 1
More informationarxiv: v1 [physics.plasmph] 3 Apr 2011
A comparison of Vlasov with drift kinetic and gyrokinetic theories arxiv:1104.0427v1 [physics.plasmph] 3 Apr 2011 H. Tasso 1, G. N. Throumoulopoulos 2 1 MaxPlanckInstitut für Plasmaphysik, Euratom Association,
More informationOn existence of resistive magnetohydrodynamic equilibria
arxiv:physics/0503077v1 [physics.plasmph] 9 Mar 2005 On existence of resistive magnetohydrodynamic equilibria H. Tasso, G. N. Throumoulopoulos MaxPlanckInstitut für Plasmaphysik Euratom Association
More informationIdeal MHD Equilibria
CapSel Equil  01 Ideal MHD Equilibria keppens@rijnh.nl steady state ( t = 0) smoothly varying solutions to MHD equations solutions without discontinuities conservative or nonconservative formulation
More informationGeorge Throumoulopoulos
George Throumoulopoulos Personal Details Born on 28 March 1956 in Fortosi, prefecture of Ioannina, Greece Family status: Married and father of two children Official address: Section of Astrogeophysics,
More information0 Magnetically Confined Plasma
0 Magnetically Confined Plasma 0.1 Particle Motion in Prescribed Fields The equation of motion for species s (= e, i) is written as d v ( s m s dt = q s E + vs B). The motion in a constant magnetic field
More informationApproximate Solutions of the GradSchlüterShafranov Equation
Approximate Solutions of the GradSchlüterShafranov Equation Gerson Otto Ludwig Associated Plasma Laboratory, National Space Research Institute 17010, São José dos Campos, SP, Brazil ludwig@plasma.inpe.br
More informationMagnetohydrodynamic stability of negative central magnetic shear, high pressure ( pol 1) toroidal equilibria
Magnetohydrodynamic stability of negative central magnetic shear, high pressure ( pol 1) toroidal equilibria Robert G. Kleva Institute for Plasma Research, University of Maryland, College Park, Maryland
More informationSimulation of alpha particle current drive and heating in spherical tokamaks
Simulation of alpha particle current drive and heating in spherical tokamaks R. Farengo 1, M. Zarco 1, H. E. Ferrari 1, 1 Centro Atómico Bariloche and Instituto Balseiro, Argentina. Consejo Nacional de
More informationStabilization of sawteeth in tokamaks with toroidal flows
PHYSICS OF PLASMAS VOLUME 9, NUMBER 7 JULY 2002 Stabilization of sawteeth in tokamaks with toroidal flows Robert G. Kleva and Parvez N. Guzdar Institute for Plasma Research, University of Maryland, College
More informationToroidal flow stablization of disruptive high tokamaks
PHYSICS OF PLASMAS VOLUME 9, NUMBER 6 JUNE 2002 Robert G. Kleva and Parvez N. Guzdar Institute for Plasma Research, University of Maryland, College Park, Maryland 207423511 Received 4 February 2002; accepted
More informationObservation of modes at frequencies above the Alfvén frequency in JET
Observation of modes at frequencies above the Alfvén frequency in JET F. Nabais 1, D. Borba 1, R. Coelho 1, L. Fazendeiro 1, J. Ferreira 1, A. Figueiredo 1, L. Fitzgerald 2, P. Rodrigues 1, S. Sharapov
More informationFormation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas )
Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas ) Yasutomo ISHII and Andrei SMOLYAKOV 1) Japan Atomic Energy Agency, Ibaraki 3110102, Japan 1) University
More informationIs the Troyon limit a beta limit?
Is the Troyon limit a beta limit? PierreAlexandre Gourdain 1 1 Extreme State Physics Laboratory, Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA The plasma beta,
More informationPropagation of Radio Frequency Waves Through Fluctuations in Plasmas
PSFC/JA15 Propagation of Radio Frequency Waves Through Fluctuations in Plasmas A. K. Ram K. Hizanidis a and S. Valvis a a National Technical University of Athens (part of HELLAS) School of Electrical
More informationMHD equilibrium calculations for stellarators. Antoine Cerfon, MIT PSFC with F. Parra, J. Freidberg (MIT NSE)
MHD equilibrium calculations for stellarators Antoine Cerfon, MIT PSFC with F. Parra, J. Freidberg (MIT NSE) March 20, 2012 MAGNETIC FIELD LINE HAMILTONIAN Consider a general toroidal coordinate system
More informationarxiv: v1 [physics.plasmph] 11 Mar 2016
1 Effect of magnetic perturbations on the 3D MHD selforganization of shaped tokamak plasmas arxiv:1603.03572v1 [physics.plasmph] 11 Mar 2016 D. Bonfiglio 1, S. Cappello 1, M. Veranda 1, L. Chacón 2 and
More informationDirect drive by cyclotron heating can explain spontaneous rotation in tokamaks
Direct drive by cyclotron heating can explain spontaneous rotation in tokamaks J. W. Van Dam and L.J. Zheng Institute for Fusion Studies University of Texas at Austin 12th USEU Transport Task Force Annual
More informationCalculation of alpha particle redistribution in sawteeth using experimentally reconstructed displacement eigenfunctions
Calculation of alpha particle redistribution in sawteeth using experimentally reconstructed displacement eigenfunctions R. Farengo, H. E. Ferrari,2, M.C. Firpo 3, P. L. GarciaMartinez 2,3, A. F. Lifschitz
More informationThe Virial Theorem, MHD Equilibria, and ForceFree Fields
The Virial Theorem, MHD Equilibria, and ForceFree Fields Nick Murphy HarvardSmithsonian Center for Astrophysics Astronomy 253: Plasma Astrophysics February 10 12, 2014 These lecture notes are largely
More informationPLASMA EQUILIBRIUM IN TOKAMAKS
PLAMA EQUILIBRIUM IN TOKAMAK H.J. de Blank FOM Institute DIFFER Dutch Institute for Fundamental Energy Research, Association EURATOMFOM, P.O. Box 27, 343 BE Nieuwegein, The Netherlands, www.differ.nl.
More informationTH/P84 Second Ballooning Stability Effect on Hmode Pedestal Scalings
TH/P84 Second Ballooning Stability Effect on Hmode Pedestal Scalings T. Onjun 1), A.H. Kritz ), G. Bateman ), A. Pankin ) 1) Sirindhorn International Institute of Technology, Klong Luang, Pathumthani,
More informationGA A23736 EFFECTS OF CROSSSECTION SHAPE ON L MODE AND H MODE ENERGY TRANSPORT
GA A3736 EFFECTS OF CROSSSECTION SHAPE ON L MODE AND H MODE ENERGY TRANSPORT by T.C. LUCE, C.C. PETTY, and J.E. KINSEY AUGUST DISCLAIMER This report was prepared as an account of work sponsored by an
More informationPropagation of Radio Frequency Waves Through Density Filaments
PSFC/JA1513 Propagation of Radio Frequency Waves Through Density Filaments A. K. Ram and K. Hizanidis a May 015 a National Technical University of Athens (part of HELLAS) School of Electrical and Computer
More informationGyrokinetic simulations of magnetic fusion plasmas
Gyrokinetic simulations of magnetic fusion plasmas Tutorial 2 Virginie Grandgirard CEA/DSM/IRFM, Association EuratomCEA, Cadarache, 13108 St PaullezDurance, France. email: virginie.grandgirard@cea.fr
More informationConfiguration Optimization of a PlanarAxis Stellarator with a Reduced Shafranov Shift )
Configuration Optimization of a PlanarAxis Stellarator with a Reduced Shafranov Shift ) Shoichi OKAMURA 1,2) 1) National Institute for Fusion Science, Toki 5095292, Japan 2) Department of Fusion Science,
More informationPOWER DENSITY ABSORPTION PROFILE IN TOKAMAK PLASMA WITH ICRH
Dedicated to Professor Oliviu Gherman s 80 th Anniversary POWER DENSITY ABSORPTION PROFILE IN TOKAMAK PLASMA WITH ICRH N. POMETESCU Association EURATOMMECTS Romania, University of Craiova, Faculty of
More informationThe RFP: Plasma Confinement with a Reversed Twist
The RFP: Plasma Confinement with a Reversed Twist JOHN SARFF Department of Physics University of WisconsinMadison Invited Tutorial 1997 Meeting APS DPP Pittsburgh Nov. 19, 1997 A tutorial on the Reversed
More informationBRIEF COMMUNICATION. Nearmagneticaxis Geometry of a Closely QuasiIsodynamic Stellarator. Greifswald, Wendelsteinstr. 1, Greifswald, Germany
BRIEF COMMUNICATION Nearmagneticaxis Geometry of a Closely QuasiIsodynamic Stellarator M.I. Mikhailov a, J. Nührenberg b, R. Zille b a Russian Research Centre Kurchatov Institute, Moscow,Russia b MaxPlanckInstitut
More informationControl of Sawtooth Oscillation Dynamics using Externally Applied Stellarator Transform. Jeffrey Herfindal
Control of Sawtooth Oscillation Dynamics using Externally Applied Stellarator Transform Jeffrey Herfindal D.A. Ennis, J.D. Hanson, G.J. Hartwell, S.F. Knowlton, X. Ma, D.A. Maurer, M.D. Pandya, N.A. Roberds,
More informationL Aquila, Maggio 2002
Nonlinear saturation of Shear Alfvén Modes and energetic ion transports in Tokamak equilibria with hollowq profiles G. Vlad, S. Briguglio, F. Zonca, G. Fogaccia Associazione EuratomENEA sulla Fusione,
More informationMagnetic Flux Surface Measurements at Wendelstein 7X
EUROFUSION WPS1PR(16) 15578 M. Otte et al. Magnetic Flux Surface Measurements at Wendelstein 7X Preprint of Paper to be submitted for publication in 43rd European Physical Society Conference on Plasma
More informationPlasmoid Motion in Helical Plasmas
Plasmoid Motion in Helical Plasmas Ryuichi ISHIZAKI and Noriyoshi NAKAJIMA National Institute for Fusion Science, Toki 5095292, Japan (Received 12 December 2009 / Accepted 18 May 2010) In order to explain
More informationHighm Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows
TH/P33 Highm Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows A. Bierwage 1), S. Benkadda 2), M. Wakatani 1), S. Hamaguchi 3), Q. Yu
More informationPlasma heating in stellarators at the fundamental ion cyclotron frequency
PHYSICS OF PLASMAS VOLUME 7, NUMBER FEBRUARY 000 Plasma heating in stellarators at the fundamental ion cyclotron frequency V. A. Svidzinski and D. G. Swanson Department of Physics, Auburn University, Auburn,
More informationSimple examples of MHD equilibria
Department of Physics Seminar. grade: Nuclear engineering Simple examples of MHD equilibria Author: Ingrid Vavtar Mentor: prof. ddr. Tomaž Gyergyek Ljubljana, 017 Summary: In this seminar paper I will
More informationComparison of Divertor Heat Flux Splitting by 3D Fields with Field Line Tracing Simulation in KSTAR
1 Comparison of Divertor Heat Flux Splitting by 3D Fields with Field Line Tracing Simulation in KSTAR W. Choe 1,2*, K. Kim 1,2, J.W. Ahn 3, H.H. Lee 4, C.S. Kang 4, J.K. Park 5, Y. In 4, J.G. Kwak 4,
More informationA simple formula for the trapped fraction in tokamaks including the effect of triangularity
A simple formula for the trapped fraction in tokamaks including the effect of triangularity O. Sauter Centre de Recherches en Physique des plasmas, Ecole Polytechnique Fédérale de Lausanne, CRPPEPFL,
More informationIterative optimisation of auxiliary coils for stellarators B.F. McMillan a, B.D. Blackwell b and J.H. Harris b a Department of Theoretical Physics, RS
Iterative optimisation of auxiliary coils for stellarators B.F. McMillan a, B.D. Blackwell b and J.H. Harris b a Department of Theoretical Physics, RSPhysSE, The Australian National University, Canberra,
More informationNumerical calculation of the Hamada basis vectors for threedimensional toroidal magnetic configurations
PHYSICS OF PLASMAS 12, 072513 2005 Numerical calculation of the Hamada basis vectors for threedimensional toroidal magnetic configurations J. N. Talmadge and S. P. Gerhardt a HSX Plasma Laboratory, University
More informationELM Suppression in DIIID Hybrid Plasmas Using n=3 Resonant Magnetic Perturbations
1 EXC/P502 ELM Suppression in DIIID Hybrid Plasmas Using n=3 Resonant Magnetic Perturbations B. Hudson 1, T.E. Evans 2, T.H. Osborne 2, C.C. Petty 2, and P.B. Snyder 2 1 Oak Ridge Institute for Science
More informationA theory for localized lowfrequency ideal MHD modes in axisymmetric toroidal systems is generalized to take into account both toroidal and poloidal
MHD spectra prehistory (selected results I MHD spectra prehistory (selected results II Abstract A theory for localized lowfrequency ideal MHD modes in axisymmetric toroidal systems is generalized to
More informationEUROFUSION WPJET1PR(16) CG Albert et al.
EUROFUSION WPJET1PR(16) 15331 CG Albert et al. Hamiltonian approach for evaluation of toroidal torque from finite amplitude nonaxisymmetric perturbations of a tokamak magnetic field in resonant transport
More informationStability of a plasma confined in a dipole field
PHYSICS OF PLASMAS VOLUME 5, NUMBER 10 OCTOBER 1998 Stability of a plasma confined in a dipole field Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received
More information(a) (b) (c) (d) (e) (f) r (minor radius) time. time. Soft Xray. T_e contours (ECE) r (minor radius) time time
Studies of Spherical Tori, Stellarators and Anisotropic Pressure with M3D 1 L.E. Sugiyama 1), W. Park 2), H.R. Strauss 3), S.R. Hudson 2), D. Stutman 4), XZ. Tang 2) 1) Massachusetts Institute of Technology,
More informationNew Schemes for Confinement of Fusion Products in Stellarators
New Schemes for Confinement of Fusion Products in Stellarators W.A. Cooper ), M.Yu. Isaev 1), M.F. Heyn 5), V.N. Kalyuzhnyj 3), S.V. Kasilov 3), W. Kernbichler 5), A.Yu. Kuyanov 1), M.I. Mikhailov 1),
More informationHeat Flux Management via Advanced Magnetic Divertor Configurations and Divertor Detachment.
Heat Flux Management via Advanced Magnetic Divertor Configurations and Divertor Detachment E. Kolemen a, S.L. Allen b, B.D. Bray c, M.E. Fenstermacher b, D.A. Humphreys c, A.W. Hyatt c, C.J. Lasnier b,
More informationTwo Fluid Dynamo and EdgeResonant m=0 Tearing Instability in Reversed Field Pinch
1 Two Fluid Dynamo and EdgeResonant m= Tearing Instability in Reversed Field Pinch V.V. Mirnov 1), C.C.Hegna 1), S.C. Prager 1), C.R.Sovinec 1), and H.Tian 1) 1) The University of WisconsinMadison, Madison,
More informationSimulation Study of Interaction between Energetic Ions and Alfvén Eigenmodes in LHD
1 Simulation Study of Interaction between Energetic Ions and Alfvén Eigenmodes in LHD Y. Todo 1), N. Nakajima 1), M. Osakabe 1), S. Yamamoto 2), D. A. Spong 3) 1) National Institute for Fusion Science,
More informationScattering of ECRF waves by edge density fluctuations and blobs
PSFC/JA147 Scattering of ECRF waves by edge density fluctuations and blobs A. K. Ram and K. Hizanidis a June 2014 Plasma Science and Fusion Center, Massachusetts Institute of Technology Cambridge, MA
More informationGlobal particleincell simulations of Alfvénic modes
Global particleincell simulations of Alfvénic modes A. Mishchenko, R. Hatzky and A. Könies MaxPlanckInstitut für Plasmaphysik, EURATOMAssociation, D749 Greifswald, Germany Rechenzentrum der MaxPlanckGesellschaft
More informationThe FieldReversed Configuration (FRC) is a highbeta compact toroidal in which the external field is reversed on axis by azimuthal plasma The FRC is
and Stability of FieldReversed Equilibrium with Toroidal Field Configurations Atomics General Box 85608, San Diego, California 921865608 P.O. APS Annual APS Meeting of the Division of Plasma Physics
More informationGA A22863 PLASMA PRESSURE AND FLOWS DURING DIVERTOR DETACHMENT
GA A22863 PLASMA PRESSURE AND FLOWS DURING DIVERTOR DETACHMENT by M.J. SCHAFFER, J.A. BOEDO, N.H. BROOKS, R.C. ISLER, and R.A. MOYER AUGUST 1998 DISCLAIMER This report was prepared as an account of work
More informationExponential Growth of Nonlinear Ballooning Instability. Abstract
Exponential Growth of Nonlinear Ballooning Instability P. Zhu, C. C. Hegna, and C. R. Sovinec Center for Plasma Theory and Computation University of WisconsinMadison Madison, WI 53706, USA Abstract Recent
More informationPhysics of fusion power. Lecture 14: Anomalous transport / ITER
Physics of fusion power Lecture 14: Anomalous transport / ITER Thursday.. Guest lecturer and international celebrity Dr. D. Gericke will give an overview of inertial confinement fusion.. Instabilities
More informationBifurcated states of a rotating tokamak plasma in the presence of a static errorfield
Bifurcated states of a rotating tokamak plasma in the presence of a static errorfield Citation: Physics of Plasmas (1994present) 5, 3325 (1998); doi: 10.1063/1.873000 View online: http://dx.doi.org/10.1063/1.873000
More informationGenerating of fusion plasma neutron source with AFSI for Serpent MC neutronics computing Serpent UGM 2015 Knoxville, TN,
Generating of fusion plasma neutron source with AFSI for Serpent MC neutronics computing Serpent UGM 2015 Knoxville, TN, 14.10.2015 Paula Sirén VTT Technical Research Centre of Finland, P.O Box 1000, 02044
More informationIMPACT OF EDGE CURRENT DENSITY AND PRESSURE GRADIENT ON THE STABILITY OF DIIID HIGH PERFORMANCE DISCHARGES
IMPACT OF EDGE CURRENT DENSITY AND PRESSURE GRADIENT ON THE STABILITY OF DIIID HIGH PERFORMANCE DISCHARGES by L.L. LAO, J.R. FERRON, E.J. STRAIT, V.S. CHAN, M.S. CHU, E.A. LAZARUS, TIC. LUCE, R.L. MILLER,
More informationEdge Momentum Transport by Neutrals
1 TH/P318 Edge Momentum Transport by Neutrals J.T. Omotani 1, S.L. Newton 1,2, I. Pusztai 1 and T. Fülöp 1 1 Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden 2 CCFE,
More informationCurrentdriven instabilities
Currentdriven instabilities Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 21 st February 2014 Ben Dudson Magnetic Confinement Fusion (1 of 23) Previously In the last
More informationFirst Observation of ELM Suppression by Magnetic Perturbations in ASDEX Upgrade and Comparison to DIIID MatchedShape Plasmas
1 PD/11 First Observation of ELM Suppression by Magnetic Perturbations in ASDEX Upgrade and Comparison to DIIID MatchedShape Plasmas R. Nazikian 1, W. Suttrop 2, A. Kirk 3, M. Cavedon 2, T.E. Evans
More informationNIMEQ: MHD Equilibrium Solver for NIMROD
NIMEQ: MHD Equilibrium Solver for NIMOD E.C.Howell, C..Sovinec University of WisconsinMadison 5 th Annual Meeting of Division of Plasma Physics Dallas, Texas, Nov. 17Nov. 1,8 1 Abstract A GradShafranov
More informationExploration of Configurational Space for Quasiisodynamic Stellarators with Poloidally Closed Contours of the Magnetic Field Strength
Exploration of Configurational Space for Quasiisodynamic Stellarators with Poloidally Closed Contours of the Magnetic Field Strength V.R. Bovshuk 1, W.A. Cooper 2, M.I. Mikhailov 1, J. Nührenberg 3, V.D.
More informationNumerical Method for the Stability Analysis of Ideal MHD Modes with a Wide Range of Toroidal Mode Numbers in Tokamaks
Numerical Method for the Stability Analysis of Ideal MHD Modes with a Wide Range of Toroidal Mode Numbers in Tokamaks Nobuyuki AIBA, Shinji TOKUDA, Takaaki FUJITA, Takahisa OZEKI, Ming S. CHU 1), Philip
More informationThe Linear Theory of Tearing Modes in periodic, cyindrical plasmas. Cary Forest University of Wisconsin
The Linear Theory of Tearing Modes in periodic, cyindrical plasmas Cary Forest University of Wisconsin 1 Resistive MHD E + v B = ηj (no energy principle) Role of resistivity No frozen flux, B can tear
More informationFrom tokamaks to stellarators: understanding the role of 3D shaping
Under consideration for publication in J. Plasma Phys. From tokamaks to stellarators: understanding the role of 3D shaping Samuel A. Lazerson and John C. Schmitt 2 Princeton Plasma Physics Laboratory,
More informationMHD Linear Stability Analysis Using a Full Wave Code
USJapan JIFT Workshop on Progress of Extended MHD Models NIFS, Toki,Japan 2007/03/27 MHD Linear Stability Analysis Using a Full Wave Code T. Akutsu and A. Fukuyama Department of Nuclear Engineering, Kyoto
More informationDynamics of charged particles in spatially chaotic magnetic fields
PSFC/JA138 Dynamics of charged particles in spatially chaotic magnetic fields Abhay K. Ram and Brahmananda Dasgupta a October 21 Plasma Science and Fusion Center, Massachusetts Institute of Technology
More informationLecture # 3. Introduction to Kink Modes the Kruskal Shafranov Limit.
Lecture # 3. Introduction to Kink Modes the Kruskal Shafranov Limit. Steve Cowley UCLA. This lecture is meant to introduce the simplest ideas about kink modes. It would take many lectures to develop the
More informationEffects of Alpha Particle Transport Driven by Alfvénic Instabilities on Proposed Burning Plasma Scenarios on ITER
Effects of Alpha Particle Transport Driven by Alfvénic Instabilities on Proposed Burning Plasma Scenarios on ITER G. Vlad, S. Briguglio, G. Fogaccia, F. Zonca Associazione EuratomENEA sulla Fusione, C.R.
More informationDIAGNOSTICS FOR ADVANCED TOKAMAK RESEARCH
DIAGNOSTICS FOR ADVANCED TOKAMAK RESEARCH by K.H. Burrell Presented at High Temperature Plasma Diagnostics 2 Conference Tucson, Arizona June 19 22, 2 134 /KHB/wj ROLE OF DIAGNOSTICS IN ADVANCED TOKAMAK
More informationPLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH
. " Reprint from PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH 1984 PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH HELD BYTHE INTERNATIONAL
More informationNIMROD simulations of dynamo experiments in cylindrical and spherical geometries. Dalton Schnack, Ivan Khalzov, Fatima Ebrahimi, Cary Forest,
NIMROD simulations of dynamo experiments in cylindrical and spherical geometries Dalton Schnack, Ivan Khalzov, Fatima Ebrahimi, Cary Forest, 1 Introduction Two experiments, Madison Plasma Couette Experiment
More informationGA A25351 PHYSICS ADVANCES IN THE ITER HYBRID SCENARIO IN DIIID
GA A25351 PHYSICS ADVANCES IN THE ITER HYBRID SCENARIO IN DIIID by C.C. PETTY, P.A. POLITZER, R.J. JAYAKUMAR, T.C. LUCE, M.R. WADE, M.E. AUSTIN, D.P. BRENNAN, T.A. CASPER, M.S. CHU, J.C. DeBOO, E.J. DOYLE,
More informationProgressing Performance Tokamak Core Physics. Marco Wischmeier MaxPlanckInstitut für Plasmaphysik Garching marco.wischmeier at ipp.mpg.
Progressing Performance Tokamak Core Physics Marco Wischmeier MaxPlanckInstitut für Plasmaphysik 85748 Garching marco.wischmeier at ipp.mpg.de Joint ICTPIAEA College on Advanced Plasma Physics, Triest,
More informationGuiding Center Orbit Studies in a Tokamak Edge Geometry Employing Boozer and Cartesian Coordinates
Contrib. Plasma Phys. 48, No. 3, 4 8 (8) / DOI./ctpp.839 Guiding Center Orbit Studies in a Tokamak Edge Geometry Employing Boozer and Cartesian Coordinates Y. Nishimura,Y.Xiao,and Z. Lin Department of
More informationMHD Simulation of High Wavenumber Ballooninglike Modes in LHD
1 TH/P916 MHD Simulation of High Wavenumber Ballooninglike Modes in LHD H. Miura and N. Nakajima National Institute for Fusion Science, 3226 Oroshi, Toki, Gifu 5095292, JAPAN email contact of main
More informationGA A26891 A FIRST PRINCIPLES PREDICTIVE MODEL OF THE PEDESTAL HEIGHT AND WIDTH: DEVELOPMENT, TESTING, AND ITER OPTIMIZATION WITH THE EPED MODEL
GA A26891 A FIRST PRINCIPLES PREDICTIVE MODEL OF THE PEDESTAL HEIGHT AND WIDTH: DEVELOPMENT, TESTING, AND ITER OPTIMIZATION WITH THE EPED MODEL by P.B. SNYDER, R.J. GROEBNER, J.W. HUGHES, T.H. OSBORNE,
More informationRWM FEEDBACK STABILIZATION IN DIII D: EXPERIMENTTHEORY COMPARISONS AND IMPLICATIONS FOR ITER
GA A24759 RWM FEEDBACK STABILIZATION IN DIII D: EXPERIMENTTHEORY COMPARISONS AND IMPLICATIONS FOR ITER by A.M. GAROFALO, J. BIALEK, M.S. CHANCE, M.S. CHU, D.H. EDGELL, G.L. JACKSON, T.H. JENSEN, R.J.
More informationTokamak elongation how much is too much? Part 1. Theory
J. Plasma Phys. (05), vol. 8, 5580607 c Cambridge University Press 05 doi:0.07/s00377850070 Tokamak elongation how much is too much? Part. Theory J. P. Freidberg,A.Cerfon and J. P Lee,, Plasma Science
More informationPredictive Study on High Performance Modes of Operation in HL2A 1
1 EX/P0 Predictive Study on High Performance Modes of Oration in HLA 1 Qingdi GAO 1), R. V. BUDNY ), Fangzhu LI 1), Jinhua ZHANG 1), Hongng QU 1) 1) Southwestern Institute of Physics, Chengdu, Sichuan,
More informationI. INTRODUCTION ISLAND COORDINATE SYSTEM
Analytical theory of the shear Alfvén continuum in the presence of a magnetic island C. R. Cook 1, a) and C. C. Hegna 1 Departments of Physics and Engineering Physics, University of WisconsinMadison,
More informationELMs and Constraints on the HMode Pedestal:
ELMs and Constraints on the HMode Pedestal: A Model Based on PeelingBallooning Modes P.B. Snyder, 1 H.R. Wilson, 2 J.R. Ferron, 1 L.L. Lao, 1 A.W. Leonard, 1 D. Mossessian, 3 M. Murakami, 4 T.H. Osborne,
More informationTH/P49. T. Takizuka 1), K. Shimizu 1), N. Hayashi 1), M. Hosokawa 2), M. Yagi 3)
1 Twodimensional Full Particle Simulation of the Flow Patterns in the Scrapeofflayer Plasma for Upper and Lower Null Point Divertor Configurations in Tokamaks T. Takizuka 1), K. Shimizu 1), N. Hayashi
More informationDT Fusion Ignition of LHDType Helical Reactor by Joule Heating Associated with Magnetic Axis Shift )
DT Fusion Ignition of LHDType Helical Reactor by Joule Heating Associated with Magnetic Axis Shift ) Tsuguhiro WATANABE National Institute for Fusion Science, 3226 Oroshicho, Toki 5095292, Japan (Received
More informationEffect of local E B flow shear on the stability of magnetic islands in tokamak plasmas
Effect of local E B flow shear on the stability of magnetic islands in tokamak plasmas R. Fitzpatrick and F. L. Waelbroeck Citation: Physics of Plasmas (1994present) 16, 052502 (2009); doi: 10.1063/1.3126964
More informationIntroduction to MagnetoHydroDynamics (MHD) Antoine Cerfon, Courant Institute, New York University
Introduction to MagnetoHydroDynamics (MHD) Antoine Cerfon, Courant Institute, New York University Email: cerfon@cims.nyu.edu SULI Introductory Course in Plasma Physics, June 6, 2016 PART I: DESCRIBING
More informationEvaluation of First Wall Heat Fluxes Due to Magnetic Perturbations for a Range of ITER Scenarios
EUROFUSION WP14ER PR(14)04 P. Cahyna et al. Evaluation of First Wall Heat Fluxes Due to Magnetic Perturbations for a Range of ITER Scenarios Preprint of Paper to be submitted for publication in Journal
More informationReducedSize LHDType Fusion Reactor with DShaped Magnetic Surface )
ReducedSize LHDType Fusion Reactor with DShaped Magnetic Surface ) Tsuguhiro WATANABE National Institute for Fusion Science, Toki 50959, Japan (Received 6 December 011 / Accepted 1 June 01) A new winding
More informationIssues in Neoclassical Tearing Mode Theory
Issues in Neoclassical Tearing Mode Theory Richard Fitzpatrick Institute for Fusion Studies University of Texas at Austin Austin, TX Tearing Mode Stability in Tokamaks According to standard (singlefluid)
More informationThe Status of the Design and Construction of the Columbia Nonneutral Torus
The Status of the Design and Construction of the Columbia Nonneutral Torus J. P. Kremer,T.S.Pedersen,N.Pomphrey,W.Reiersen and F. Dahlgren Dept. of Applied Physics and Applied Mathematics, Columbia University,
More informationCollisionless nonideal ballooning modes
PHYSICS OF PLASMAS VOLUME 6, NUMBER 1 JANUARY 1999 Collisionless nonideal ballooning modes Robert G. Kleva and Parvez N. Guzdar Institute for Plasma Research, University of Maryland, College Park, Maryland
More informationImproved Analytical Flux Surface Representation and Calculation Models for Poloidal Asymmetries. T. G. Collart, W. M. Stacey
Improved Analytical Flux Surface Representation and Calculation Models for Poloidal Asymmetries T. G. Collart, W. M. Stacey Georgia Institute of Technology Atlanta, GA 3332 USA December, 215 Abstract An
More informationPlasma turbulence measured by fast sweep reflectometry on TORE SUPRA
Plasma turbulence measured by fast sweep reflectometry on TORE SUPRA F. Clairet &, L. Vermare &, S. Heuraux, G. Leclert # & Association EuratomCEA sur la fusion, DSM/DRFC/SCCP C.E. Cadarache, 8 SaintPaullèsDurance,
More informationExact solutions for magnetic annihilation in curvilinear geometry
Exact solutions for magnetic annihilation in curvilinear geometry E. Tassi b,, V.S. Titov and G. Hornig Theoretische Physik IV, RuhrUniversität Bochum, 44780 Bochum, Germany b Theoretische Physik IV,
More informationRole of the mean curvature in the geometry of magnetic confinement configurations
arxiv:1008.1567v2 [physics.plasmph] 11 Aug 2010 Role of the mean curvature in the geometry of magnetic confinement configurations A.A. Skovoroda I.A. Taimanov Abstract Examples are presented of how the
More informationTurbulence in Tokamak Plasmas
ASDEX Upgrade Turbulence in Tokamak Plasmas basic properties and typical results B. Scott Max Planck Institut für Plasmaphysik Euratom Association D85748 Garching, Germany Uni Innsbruck, Nov 2011 Basics
More information