Stability theory of dissipative trapped-electron and trapped-ion modes

Horton, W.; Ross, D. W.; Tang, W.M.; Berk, H. L.; Frieman, E. A.; Laquey, R. E.; Lovelace, R. V. E.; Mahajan, S. M.; Rosenbluth, M. N.; Rutherford, P. H.

doi:10.2172/4202907

Cited by 9 publications

(21 citation statements)

References 3 publications

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“…l4> m l= l* m ±l'> etc -)-In t n e present calculation, the fact that A <0 and D/a 2 >0 in Eq. (83) indicates that this onset condition for a mode, which is insensitive to shear and which is localized at the magnetic field minimum, implies the requirement that the shear be sufficiently weak, i.e. s < 1/2.…”

Section: Ay 'mentioning

confidence: 99%

“…( 68) have, in general, followed the procedure introduced by Pearlstein and Berk [15] for collisionless drift instabilities. In their analysis as well as in analogous studies of trapped-electron modes [82,83], the circulating electron term, R(x), is taken to be a first-order quantity. Hence, to lowest order, the radial equation reduces to the Weber equation which has solutions of the form…”

Section: Radial Analysis-idmentioning

confidence: 99%

“…In subsequent work, Liu, et al [21 ] and Deschamps, et al [114] found that even in the absence of temperature gradients, the finite-ion-gyroradius shift of the mode frequency below o>* could lead to dissipative trapped-electron modes analogous to the universal modes. Galeev and Sagdeev's radial calculations were extended to include this effect by Liu, et al [21 ] and by Horton, et al [83]. However, Sauthoff, et al [115] have noted that the stabilizing influence of shear could be ineffective if the diamagnetic frequency profile is sufficiently peaked.…”

Section: Trapped-electron Modesmentioning

confidence: 99%

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Microinstability theory in tokamaks

1978

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Significant investigations in the area of tokamak microinstability theory are reviewed. Special attention is focused on low-frequency electrostatic drift-type modes, which are generally believed to be the dominant tokamak microinstabilities under normal operating conditions. The basic linear formalism including electromagnetic (finite-beta) modifications is presented along with a general survey of the numerous papers investigating specific linear and non-linear effects on these modes. Estimates of the associated anomalous transport and confinement times are discussed, and a summary of relevant experimental results is given. Studies of the non-electrostatic and high-frequency instabilities associated with the presence of high-energy ions from neutral-beam injection (or with the presence of alpha-particles from fusion reactions) are also surveyed.

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Section: Ay 'mentioning

confidence: 99%

Section: Radial Analysis-idmentioning

confidence: 99%

Section: Trapped-electron Modesmentioning

confidence: 99%

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Microinstability theory in tokamaks

1978

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“…the order of the largest fluid velocity at each order in the perturbation expansion. Therefore, collisional drag has very little influence on v~l) for v+ << n. , and to good -J ,- They have been included in a preliminary two dimensional study [14]. where .…”

Section: -Ymentioning

confidence: 99%

“…The " /L2 yp -and £ -m/L . We also define yp ' characteristic equation then becomes det ( i~ ~ + ~) = 0 , (14) where Iij = oij and Dij(E,f) = yP.+(N+l~i)oij-[£+(N+l-i)]ai-i , and we retain in the equilibrium the amplitudes anL'n=l,2, ... ,N.…”

Section: Saturated States: Dispersionless and Collisionless (V++o) Limitmentioning

confidence: 99%

Nonlinear saturation of the dissipative trapped-ion mode by mode coupling

Cohen¹,

Krommes²,

Tang³

et al. 1976

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The nonlinear saturation of the dissipative trapped-ion mode is analyzed. . I The basic mechanism considered is the process whereby energy in long wavelength th unstable modes is nonlinearly coupled via E x B convection to short wavelength modes stabilized by Landau damping due to both circulating and trapped ions. In the usual limit of the mode frequency small relative to the effective electron collision frequency, a one-dimensional nonlinear partial differential equation for the potential can be derived, as first shown by LaQuey, Mahajan, Tang, and Rutherford. The stability and accessibility of the possible equilibria for this equation are examined in detail, both analytically and numerically. The equilibrium emphasized by LaQuey et al. is shown to be unstable. However, a class of nonlinear saturated states which are stable to linear perturbations is found. Included in the analysis are the effects of both ion collisions and dispersion due to finite ion bananawidth effects. Cross-field transport is estimated and the scaling of the results is considered for tokamak parameters (specifically those for the'• Princeton Large Torus). It is concluded that the anomalous• cross-field transport can be much lower than the estimate of Kadomtsev and Pogutse, for relevant parameters.

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Finite-beta and resonant-electron effects on trapped-electron instabilities

et al. 1976

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Finite-6 (plasma pressure/magnetic pressure) and resonant electron effects on the dissipative trapped-electron instabilities are analysed. These modifications are shown to have a strong stabilizing influence on the finite-ion-gyroradiusand electron-temperature-gradient-driven modes, respectively. For relevant tokamak parameters, complete stabilization may be possible. Stability criteria for radially local and non-local cases are presented.

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Stability theory of dissipative trapped-electron and trapped-ion modes

Cited by 9 publications

References 3 publications

Microinstability theory in tokamaks

Microinstability theory in tokamaks

Nonlinear saturation of the dissipative trapped-ion mode by mode coupling

Finite-beta and resonant-electron effects on trapped-electron instabilities

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