Ideal magnetohydrodynamic theory of magnetic fusion systems

Ideal magnetohydrodynamic theory and its application to magnetic fusion systems are reviewed. The review begins with a description and derivation of the model as well as a discussion of the region of validity. Next, the general properties are derived. These are valid for arbitrary geometry and demonstrate the inherently sound physical foundation of the model. The equilibrium behavior of the currently most promising toroidal magnetic fusion concepts are then discussed in detail. Finally, the stability of such equilibria is investigated. Included are discussions of the general stability properties of arbitrary magnetic geometries and of detailed applications to those concepts of current fusion interest.

[1]  Martin Schwarzschild,et al.  Some instabilities of a completely ionized plasma , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  W. Newcomb.  Motion of magnetic lines of force , 1958 .

[3]  F. Low,et al.  The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  J. Lawson.  SOME CRITERIA FOR A POWER PRODUCING THERMONUCLEAR REACTOR , 1957 .

[5]  M. Rosenbluth,et al.  Stability of plasmas confined by magnetic fields , 1957 .

[6]  E. A. Frieman,et al.  An energy principle for hydromagnetic stability problems , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  K. Hain,et al.  Zur Stabilität zylindersymmetrischer Plasmakonfigurationen mit Volumenströmen , 1958 .

[8]  L. Woltjer.  HYDROMAGNETIC EQUILIBRIUM II. STABILITY IN THE VARIATIONAL FORMULATION. , 1959, Proceedings of the National Academy of Sciences of the United States of America.

[9]  C. Mercier,et al.  A necessary condition for hydromagnetic stability of plasma with axial symmetry , 1960 .

[10]  W. Newcomb.  HYDROMAGNETIC STABILITY OF A DIFFUSE LINEAR PINCH , 1960 .

[11]  John L. Johnson,et al.  Determination of Hydromagnetic Equilibria , 1961 .

[12]  Stability Criterion for Arbitrary Hydromagnetic Equilibria , 1962 .

[13]  Harold P. Furth,et al.  Finite‐Resistivity Instabilities of a Sheet Pinch , 1963 .

[14]  S. Yoshikawa.  Application of the Virial Theorem to Equilibria of Toroidal Plasmas , 1964 .

[15]  C. Mercier,et al.  Necessity of the energy principles for magnetostatic stability , 1965 .

[16]  F. Haas,et al.  Stability of a Circular Toroidal Plasma under Average Magnetic Well Conditions , 1966 .

[17]  H. Grad.  TOROIDAL CONTAINMENT OF A PLASMA. , 1967 .

[18]  H. Grad.  Magneto-Fluid and Plasma Dynamics , 1967 .

[19]  John L. Johnson,et al.  Interchange instabilities in ideal hydromagnetic theory , 1968 .

[20]  K. E. Weimer,et al.  Application of the energy principle to Astron-type and other axisymmetric devices , 1969 .

[21]  K. E. Weimer,et al.  Stability Limitations for Stellarators with Sharp Surfaces , 1969 .

[22]  D. Lortz.  Über die Existenz toroidaler magnetohydrostatischer Gleichgewichte ohne Rotationstransformation , 1970 .

[23]  Instability of the m = 1 Mode of a Rotating θ Pinch , 1970 .

[24]  M. Rosenbluth,et al.  2.6 Feedback Stabilization of a High‐β, Sharp‐Boundaried Plasma Column with Helical Fields , 1970 .

[25]  G. Laval,et al.  BALLOONING MODES IN AXISYMMETRIC TOROIDAL CONFIGURATIONS. , 1970 .

[26]  M. Haines,et al.  Application of Finite Larmor Radius Equations for Collisionless Plasmas to a θ Pinch , 1971 .

[27]  Vitalii D. Shafranov,et al.  Plasma equilibrium in a Tokamak , 1971 .

[28]  Critical beta for Toroidal Equilibrium , 1971 .

[29]  V. Shafranov,et al.  Determination of the parameters βI and li in a Tokamak for arbitrary shape of plasma pinch cross-section , 1971 .

[30]  D. Robinson.  High-β diffuse pinch configurations , 1971 .

[31]  F. L. Ribe,et al.  Fusion reactor systems , 1972 .

[32]  J. D. Callen,et al.  Magnetohydrodynamic Equilibria in Sharply Curved Axisymmetric Devices , 1972 .

[33]  F. Haas.  Sharp‐Boundary Model of a High‐Pressure Tokamak , 1972 .

[34]  H. Grad.  Magnetofluid-dynamic spectrum and low shear stability. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[35]  J. Freidberg,et al.  Stability of two‐dimensional magnetohydrodynamic equilibria , 1973 .

[36]  J. Brackbill,et al.  An implicit, almost-Lagrangian algorithm for magnetohydrodynamics , 1973 .

[37]  Sufficient stability criteria for general MHD-equilibria , 1973 .

[38]  Comparison Between Necessary and Sufficient Stability Criteria for Axially Symmetric Equilibria , 1973 .

[39]  M. Rosenbluth,et al.  Nonlinear properties of the internal m = 1 kink instability in the cylindrical tokamak , 1973 .

[40]  J. Freidberg,et al.  Kink instabilities in a high‐β tokamak , 1973 .

[41]  A. Sykes,et al.  Two-dimensional calculation of tokamak stability , 1974 .

[42]  A.B. Mikhailovskij.  Tokamak stability at high plasma pressures , 1974 .

[43]  Improved sufficient conditions for magnetohydrodynamic stability with closed field lines , 1974 .

[44]  J. Freidberg,et al.  Kink instabilities in a high‐β tokamak with elliptic cross section , 1974 .

[45]  J. B. Taylor,et al.  Relaxation of toroidal plasma and generation of reverse magnetic fields , 1974 .

[46]  R. Kristal,et al.  Plasma equilibrium and stability in the Scyllac toroidal sector experiments , 1974 .

[47]  P. H. Sakanaka,et al.  New approach to magnetohydrodynamic stability: II. Sigma‐stable diffuse pinch configurations , 1974 .

[48]  W. Schneider,et al.  MHD instabilities as an initial boundary-value problem , 1974 .

[49]  P. H. Sakanaka,et al.  New approach to magnetohydrodynamic stability. I. A practical stability concept , 1974 .

[50]  G. Laval,et al.  Hydromagnetic stability of a current‐carrying pinch with noncircular cross section , 1974 .

[51]  High-beta stellarator experiments on ISAR T1 , 1975 .

[52]  E. Rebhan.  Stability boundaries of tokamaks with respect to rigid displacements , 1975 .

[53]  J. P. Goedbloed.  Spectrum of ideal magnetohydrodynamics of axisymmetric toroidal systems , 1975 .

[54]  Stability of a diffuse, high β, l=1 system , 1975 .

[55]  F. Haas.  Stability of a high-β tokamak to uniform vertical displacements , 1975 .

[56]  J. L. Soule,et al.  Internal kink modes in toroidal plasmas with circular cross sections , 1975 .

[57]  P. Garabedian,et al.  Equilibrium and stability code for a diffuse plasma. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[58]  F. Hinton,et al.  Theory of plasma transport in toroidal confinement systems , 1976 .

[59]  G. Miller.  Long wavelength m=1 magnetohydrodynamics of a theta pinch , 1977 .

[60]  MHD stability of toroidal equilibria to axisymmetric modes , 1977 .

[61]  J. Wesson,et al.  High-. beta. tokamaks , 1977 .

[62]  A. H. Glasser,et al.  Theory of ballooning modes in tokamaks with finite shear , 1977 .

[63]  D. E. Baldwin,et al.  End-loss processes from mirror machines , 1977 .

[64]  John L. Johnson,et al.  Stability limitations on high-beta Tokamaks , 1977 .

[65]  J. Freidberg,et al.  Finite‐gyroradius stabilization of diffuse high beta stellarators , 1977 .

[66]  Yueng Kay Martin Peng,et al.  High-pressure flux-conserving tokamak equilibria , 1977 .

[67]  B. Coppi.  Topology of ballooning modes , 1977 .

[68]  Computation of Magnetohydrodynamic Flow in a Magnetically Confined Plasma , 1977 .

[69]  J. F. Clarke,et al.  High-Pressure Flux-Conserving Tokamak Equilibria , 1977 .

[70]  G. L. Jahns,et al.  Experimental Measurement of Electron Heat Diffusivity in a Tokamak , 1977 .

[71]  G. L. Jahns,et al.  Internal disruptions in tokamaks , 1977 .

[72]  N. Fisch.  Confining a Tokamak Plasma with rf-Driven Currents. , 1978 .

[73]  l=1,2 high-beta stellarator , 1978 .

[74]  Kenro Miyamoto,et al.  Recent stellarator research , 1978 .

[75]  G. Spies.  Magnetohydrodynamic spectrum of instabilities due to plasma rotation , 1978 .

[76]  J. Freidberg,et al.  Rotational instabilities in a theta pinch , 1978 .

[77]  J. Wesson.  Hydromagnetic stability of tokamaks , 1978 .

[78]  F. J. Helton,et al.  MHD equilibrium in non-circular tokamaks with field-shaping coil systems , 1978 .

[79]  J. W. Connor,et al.  Shear, periodicity, and plasma ballooning modes , 1978 .

[80]  J. Freidberg,et al.  Finite Larmor radius equations in an arbitrary near‐theta pinch geometry , 1978 .

[81]  J. P. Goedbloed,et al.  High‐beta tokamaks surrounded by force‐free fields , 1978 .

[82]  Asymptotic theory of diffuse high-beta magnetohydrostatic equilibria in three dimensions , 1978 .

[83]  B. V. Waddell,et al.  Mechanism for Major Disruptions in Tokamaks , 1978 .

[84]  R. A. Dory,et al.  Stability study of high-. beta. flux-conserving equilibria , 1979 .

[85]  Secular instability of MHD equilibria in a magnetic quadrupole field , 1979 .

[86]  B. V. Waddell,et al.  Nonlinear interaction of tearing modes in highly resistive tokamaks , 1979 .

[87]  Unstable Continuous Spectrum and Ballooning Modes , 1979 .

[88]  R. L. Miller,et al.  Shape optimization of tokamak plasmas to localized magnetohydrodynamic modes , 1979 .

[89]  J. Manickam,et al.  Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria , 1979 .

[90]  Macroscopic stability and beta limit in the ELMO Bumpy Torus , 1979 .

[91]  D. E. Baldwin,et al.  Improved tandem mirror fusion reactor , 1979 .

[92]  Finite-. beta. /sub e/ universal-mode turbulence and Alcator scaling , 1979 .

[93]  D. B. Nelson,et al.  Staircase model for magnetohydrodynamic spectrum and global instabilities in the Elmo bumpy torus , 1979 .

[94]  R. J. Hastie,et al.  High mode number stability of an axisymmetric toroidal plasma , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[95]  E. Hameiri.  Shear stabilization of the Rayleigh–Taylor modes , 1979 .

[96]  Equilibria of diffuse high beta stellarators , 1979 .

[97]  Dependence of ideal-MHD kink and ballooning modes on plasma shape and profiles in tokamaks , 1979 .

[98]  R. Commisso,et al.  Collisionless flow and end loss from a high‐energy theta‐pinch plasma , 1980 .

[99]  TOROIDAL MHD EQUILIBRIUM OF THE ELMO BUMPY TORUS , 1980 .

[100]  A. A. Newton,et al.  Reversed-field-pinch research , 1980 .

[101]  L. Bernard,et al.  Stabilization of ideal MHD modes , 1980 .

[102]  D. B. Nelson.  Effects of hot electrons on magnetohydrodynamic modes in ELMO Bumpy Torus , 1980 .

[103]  A. Reiman.  Minimum energy state of a toroidal discharge , 1980 .

[104]  W Vii-A Team,et al.  Stabilization of the (2, 1) tearing mode and of the current disruption in the W VII–A stellarator , 1980 .

[105]  Necessary and sufficient magnetohydrodynamic stability criterion for rotating multipoles and mirrors , 1980 .

[106]  L. Spitzer.  The Stellarator Concept , 1958, IEEE Transactions on Plasma Science.