A reduced set of magnetohydrodynamic (MHD) equations is derived, applicable to large aspect ratio... more A reduced set of magnetohydrodynamic (MHD) equations is derived, applicable to large aspect ratio tokamaks and relevant for dynamics that is sub-Alfvénic with respect to ideal ballooning modes. This ordering optimally allows sound waves, Mercier modes, drift modes, geodesic-acoustic modes (GAM), zonal flows and shear Alfvén waves. Wavelengths long compared to the gyroradius but comparable to the minor radius of a typical tokamak are considered. With the inclusion of resistivity, tearing modes, resistive ballooning modes, Pfirsch–Schluter cells and the Stringer spin-up are also included. A major advantage is that the resulting system is two-dimensional in space, and the system incorporates self-consistent and dynamic Shafranov shifts. A limitation is that the system is valid only in radial domains where the tokamak safety factor, $q$ , is close to rational. In the tokamak core, the system is well suited to study the sawtooth discharge in the presence of Mercier modes. The systematic ...
A fluid theory of collisional electrostatic drift waves in a plasma slab with magnetic shear is p... more A fluid theory of collisional electrostatic drift waves in a plasma slab with magnetic shear is presented. Both electron temperature and density gradients are included. The equations are solved analytically in all relevant regions of the parameter space defined by the magnetic shear strength and the perpendicular wavelength and explicit expressions for the growth rates are given. For shear strengths appropriate for present-day tokamak discharges the temperature gradient produces potential wells which localize the mode in the electron resistive region, well inside the ion sound turning points. Mode stability arises from a competition between the destabilizing influence of the time dependent thermal force and the stabilizing influence of electron energy dissipation. Convective energy loss is not important for shear parameters of present-day fusion devices.
The poloidal rotation of tokamak plasmas is studied in the plateau regime. It is shown that the r... more The poloidal rotation of tokamak plasmas is studied in the plateau regime. It is shown that the relaxation rate is given by vT/(qR)ν̂1/3O(1), while the inertia enhancement in this regime is 1+q2ν̂−1/3O(1), resulting from the time-dependent parallel viscosity, where q is the safety factor, ν̂=ε3/2ν* is the plateau collisionality parameter (ε3/2<ν̂<1), ε is the inverse aspect ratio, and ν* is the standard neoclassical collisionality parameter. An evolutionary equation for the radial electric field is derived.
An investigation of the ion temperature gradient instability that focuses on the behavior of the ... more An investigation of the ion temperature gradient instability that focuses on the behavior of the mode when it is weakly unstable is presented. It is shown that ηi= (2)/(3) is the threshold for long wavelength instability, ηi being the ratio of the density gradient scale length to the ion temperature gradient scale length. For ηi>0.902, a short wavelength mode is concomitantly unstable. The transport resulting from both the short and the long wavelengths is shown to constitute a ‘‘soft’’ turn on of anomalous transport for ηi<2, with long (short) wavelengths dominating for high (weak) enough collisionality. The point ηi=2 represents a ‘‘hard’’ threshold for transport: Beyond this point, large, collisionless transport over all wavelengths is precipitated. A nonlocal collisional theory as well as a kinetic theory with a Krook collision operator are presented to describe the progression from weak to strong instability. Transport estimates, based on mixing length arguments, are give...
A set of one-fluid, modified magnetohydrodynamic (MHD) equations is developed that describes magn... more A set of one-fluid, modified magnetohydrodynamic (MHD) equations is developed that describes magnetized plasmas for which the relevant scale lengths are intermediate between the electron and ion Larmor radii, and the relevant time scales are intermediate between the electron and ion cyclotron frequencies. It is shown that the momentum equation is the same as that of conventional MHD but that the evolution of the magnetic field is strongly affected. The implications of the modified MHD system on the ‘‘frozen-in’’ theorem, magnetosonic waves, Alfvén waves, and the interchange instability are examined.
Kinetic and fluid approaches to the problem of low-frequency magnetohydrodynamic flute stability ... more Kinetic and fluid approaches to the problem of low-frequency magnetohydrodynamic flute stability of plasmas where the equilibrium electron gradient-B drift is larger than the curvature drift are compared. It is shown that the two approaches are practically identical for frequencies below the curvature drift frequency. The identical nature of the approaches has to do with the fact that the large gradient-B drift has the primary effect of maintaining the electron temperature constant along its path; since this fact is independent of the collision frequency, the same equation of state applies to both approaches.
A comprehensive theoretical treatment of the linear stability of a sub-Alfvénic plasma expansion ... more A comprehensive theoretical treatment of the linear stability of a sub-Alfvénic plasma expansion is developed. The analysis is similar to those performed for the lower-hybrid-drift instability and the drift cyclotron instability. In addition to the diamagnetic drift (Vdi) that drives these instabilities, the gravitational drift (Vg) caused by the deceleration of the plasma shell, and the Pedersen drift (VP) caused by ion–neutral collisions and neutral gas flow, are included. The emphasis of the paper is on the instability driven by the gravitational drift. The theory is fully kinetic and includes finite-beta effects (i.e., electromagnetic coupling and electron ∇B drift-wave resonances), collisional effects (electron–ion, electron–neutral, and ion–neutral collisions), and neutral gas flow, effects that have not been considered to date. The analysis is carried out in a slab geometry although the applications are to spherical expansions. The main conclusions are as follows. In the stro...
A tokamak plasma rotating poloidally at speeds in excess of the poloidal sound speed is studied. ... more A tokamak plasma rotating poloidally at speeds in excess of the poloidal sound speed is studied. The study is motivated by the propositions that shear in the rotation could suppress turbulence and improve confinement and that the poloidal sound speed is the critical speed to exceed for flow profiles distributed over the entire minor radius. For such rapidly rotating plasma regimes, the Grad-Shafranov equation is examined, the damping rate of the rotation is calculated, particle orbits are investigated, and a heuristic MHD stability study is done. It is found that for rotation speeds exceeding the poloidal sound speed but less than the poloidal Alfven speed no deleterious effects can be expected from the rapid rotation as regards equilibrium or MHD stability. The damping rate of poloidal rotation is shown to fall off over the peak rate, in all collisionality regimes, as up-2. This feature makes more efficacious the external driving of such poloidal flow and allows favourable extrapolation to reactor relevant regimes. Finally, it is shown that the fraction of trapped ions is significantly depleted in this regime, suggesting a reduction in the neoclassical heat transport as well
The convection of a magnetically confined plasma resulting from heat and particle sources is stud... more The convection of a magnetically confined plasma resulting from heat and particle sources is studied. It is assumed that the convection is low-level in that the system stays stable to ideal interchange instabilities. A Z-pinch plasma with asymmetric particle and heat sources is considered. It is found that there is no convection if there are no particle sources, independent of the distribution of the heat sources. Particle sources result in convection which in turn influences heat transport. The central temperature, however, may go up or down in response to this convection, depending on the distribution of the source function.
Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrate... more Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfvén wave, and an initial value code solves the resulting equations. The s−α diagram (magnetic shear versus pressure gradient) of ballooning mode theory is extended to include rotational shear. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (dΩ/dq, where Ω is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and direct stable access to the second stability regime occurs when this frequency is approximately one-quarter to one-half the Alfvén frequency, ωA=VA/qR.
The basic idea of centrifugal confinement is to use centrifugal forces from supersonic rotation t... more The basic idea of centrifugal confinement is to use centrifugal forces from supersonic rotation to augment conventional magnetic confinement. Optimizing this “knob” results in a fusion device that features four advantages: steady state, no disruptions, superior cross-field confinement, and a simpler coil configuration. The idea rests on two prongs: first, centrifugal forces can confine plasmas to desired regions of shaped magnetic fields; second, the accompanying large velocity shear can stabilize even magnetohydrodynamic (MHD) instabilities. A third feature is that the velocity shear also viscously heats the plasma; no auxiliary heating is necessary to reach fusion temperatures. Regarding transport, the velocity shear can also quell microturbulence, leading to fully classical confinement, as there are no neoclassical effects. Classical parallel electron transport then sets the confinement time. These losses are minimized by a large Pastukhov factor resulting from the deep centrifug...
A new instability is proposed to instability which can explain the large-scale explain the observ... more A new instability is proposed to instability which can explain the large-scale explain the observed large-scale structuring of the structuring of the AMPTE magnetotail barium magnetotail AMPTE barium releases. The stability releases. The new instability is obtained by using theory is based on a modified set of MHD equations a set of one-fluid equations that is more which allows for large Larmor radius effects, i.e., appropriate for Pi ~ Rc than the ideal MHD Pi ~ R c which is typical of the AMPTE releases equations. The instability is a fluid mode that (here •i is the ion Larmor radius and R_ is the transverse radius of the cloud). The mo•e is driven by the deceleration of the cloud and the density gradient at the edge of the cloud. The predicted linear growth rate and eigenmode structure are consistent with AMPTE observations.
Recent studies of transient reconnection show presence of dipolarization fronts which are charact... more Recent studies of transient reconnection show presence of dipolarization fronts which are characterized by a steep increase or jump in the z component of the earth's tail magnetic field. This has been reported in satellite data as well as kinetic simulations. One possible interpretation of these jumps is the formation of shocks using the standard MHD Rankine-Hugoniot relations. Furthermore in
The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermon... more The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermonuclear fusion. The device is steady state, there are no disruptions, the loss cone is almost closed, sheared rotation stabilizes magnetohydrodynamic (MHD) instabilities as well as plasma turbulence, and the coil configuration is simple. In this work we examine the effect of rotation on mirror confinement using a full cyclotron orbit code. The full cyclotron simulations give a much more complete description of the particle energy distribution and losses than the use of guiding center equations. Both collisionless loss as a function of rotation and the effect of collisions are investigated. Although the cross field diffusion is classical, we find that the local rotating Maxwellian is increased to higher energy, increasing the fusion rate and also enhancing the radial diffusion. We find a loss channel not envisioned with a guiding center treatment, but a design can be chosen that can satisfy the Lawson criterion for ions. Of course, the rotation has minimal effect on the alpha particle birth distribution, so there is initially loss through the usual loss cone, just as in a mirror with no rotation. However after this loss the alphas slow down on the electrons with little pitch angle scattering until reaching low energy, so over half of the initial alpha energy is transfered to the electrons. The important problem of energy confinement, with losses primarily through the electron channel, is not addressed in this work. We also discuss the use of rotating mirror geometry to produce an ion thruster.
APS Division of Plasma Physics Meeting Abstracts, Nov 1, 1997
The Maryland Centrifugal Torus (MCT) is proposed to test the possibility of using centrifugal for... more The Maryland Centrifugal Torus (MCT) is proposed to test the possibility of using centrifugal forces of rotating plasma as an effective "gravitational" potential to confine plasma along the magnetic field. Thus, the rotation consititutes an additional "knob" to aid magnetic confinement. We consider here the underlying theoretical concerns. The flowing MHD equilibrium is studied. Analytical as well as numerical results are presented: "gravitational" confinement is demonstrated. An MHD stability study is summarized: it is shown that a toroidal magnetic field might be essential to achieve complete stability to convective MHD modes. The critical field required for stability is one of the objectives of the MCT experiment. Preliminary results from a numerical experiment to test the stabilization of MHD modes by the large velocity shear will be presented. The scaling of centrifugally confined plasmas to fusion reactors will be assessed. Neoclassical transport is estimated to show that the Lawson Condition is achievable in principle. The advantages of the system - steady state, disruption-free, superior confiement, and simpler coil system - are discussed in conjunction with the disadvantages - large circulating power, alpha losses, insulating first wall.
Submitted for the APR12 Meeting of The American Physical Society Double adiabatic theory of drive... more Submitted for the APR12 Meeting of The American Physical Society Double adiabatic theory of driven collisionless geodesic acoustic modes (GAMs) in toroids 1 ADIL HASSAM, ROBERT KLEVA, WRICK SEN-GUPTA, University of Maryland-The GAM is an axisymmetric oscillation of a toroidal magnetically confined plasma, resulting from an interplay between poloidal plasma rotation and perpendicular flux tube compression from the B field gradient. The frequency is super-parallel-sonic, ie, ω ∼ (ion thermal speed)/R, greater than the parallel acoustic mode which is lower by a factor of q. Consequently, collisionless geodesic acoustic modes in tokamaks can be described by the Chew-Goldberger-Low double-adiabatic fluid closures. This allows a simpler nonlinear formulation. We use these equations to study driven, collisionless GAMs in tokamaks. The motivation for this study is a proposal by Hallatschek and McKee to drive GAMs on the D3D tokamak at resonance. The drivers in the CGL theory include external magnetic forces to effect flux surface displacements as well as sources to provide modulated non-axisymmetric ion heating. We show that the linear mode frequency from CGL theory agrees with previous kinetic results. Comparisons will be made between different approaches to resonate the mode. Nonlinear effects will be evaluated. Results of a 2D toroidal numerical simulation of driven GAMs are described
A reduced set of magnetohydrodynamic (MHD) equations is derived, applicable to large aspect ratio... more A reduced set of magnetohydrodynamic (MHD) equations is derived, applicable to large aspect ratio tokamaks and relevant for dynamics that is sub-Alfvénic with respect to ideal ballooning modes. This ordering optimally allows sound waves, Mercier modes, drift modes, geodesic-acoustic modes (GAM), zonal flows and shear Alfvén waves. Wavelengths long compared to the gyroradius but comparable to the minor radius of a typical tokamak are considered. With the inclusion of resistivity, tearing modes, resistive ballooning modes, Pfirsch–Schluter cells and the Stringer spin-up are also included. A major advantage is that the resulting system is two-dimensional in space, and the system incorporates self-consistent and dynamic Shafranov shifts. A limitation is that the system is valid only in radial domains where the tokamak safety factor, $q$ , is close to rational. In the tokamak core, the system is well suited to study the sawtooth discharge in the presence of Mercier modes. The systematic ...
A fluid theory of collisional electrostatic drift waves in a plasma slab with magnetic shear is p... more A fluid theory of collisional electrostatic drift waves in a plasma slab with magnetic shear is presented. Both electron temperature and density gradients are included. The equations are solved analytically in all relevant regions of the parameter space defined by the magnetic shear strength and the perpendicular wavelength and explicit expressions for the growth rates are given. For shear strengths appropriate for present-day tokamak discharges the temperature gradient produces potential wells which localize the mode in the electron resistive region, well inside the ion sound turning points. Mode stability arises from a competition between the destabilizing influence of the time dependent thermal force and the stabilizing influence of electron energy dissipation. Convective energy loss is not important for shear parameters of present-day fusion devices.
The poloidal rotation of tokamak plasmas is studied in the plateau regime. It is shown that the r... more The poloidal rotation of tokamak plasmas is studied in the plateau regime. It is shown that the relaxation rate is given by vT/(qR)ν̂1/3O(1), while the inertia enhancement in this regime is 1+q2ν̂−1/3O(1), resulting from the time-dependent parallel viscosity, where q is the safety factor, ν̂=ε3/2ν* is the plateau collisionality parameter (ε3/2<ν̂<1), ε is the inverse aspect ratio, and ν* is the standard neoclassical collisionality parameter. An evolutionary equation for the radial electric field is derived.
An investigation of the ion temperature gradient instability that focuses on the behavior of the ... more An investigation of the ion temperature gradient instability that focuses on the behavior of the mode when it is weakly unstable is presented. It is shown that ηi= (2)/(3) is the threshold for long wavelength instability, ηi being the ratio of the density gradient scale length to the ion temperature gradient scale length. For ηi>0.902, a short wavelength mode is concomitantly unstable. The transport resulting from both the short and the long wavelengths is shown to constitute a ‘‘soft’’ turn on of anomalous transport for ηi<2, with long (short) wavelengths dominating for high (weak) enough collisionality. The point ηi=2 represents a ‘‘hard’’ threshold for transport: Beyond this point, large, collisionless transport over all wavelengths is precipitated. A nonlocal collisional theory as well as a kinetic theory with a Krook collision operator are presented to describe the progression from weak to strong instability. Transport estimates, based on mixing length arguments, are give...
A set of one-fluid, modified magnetohydrodynamic (MHD) equations is developed that describes magn... more A set of one-fluid, modified magnetohydrodynamic (MHD) equations is developed that describes magnetized plasmas for which the relevant scale lengths are intermediate between the electron and ion Larmor radii, and the relevant time scales are intermediate between the electron and ion cyclotron frequencies. It is shown that the momentum equation is the same as that of conventional MHD but that the evolution of the magnetic field is strongly affected. The implications of the modified MHD system on the ‘‘frozen-in’’ theorem, magnetosonic waves, Alfvén waves, and the interchange instability are examined.
Kinetic and fluid approaches to the problem of low-frequency magnetohydrodynamic flute stability ... more Kinetic and fluid approaches to the problem of low-frequency magnetohydrodynamic flute stability of plasmas where the equilibrium electron gradient-B drift is larger than the curvature drift are compared. It is shown that the two approaches are practically identical for frequencies below the curvature drift frequency. The identical nature of the approaches has to do with the fact that the large gradient-B drift has the primary effect of maintaining the electron temperature constant along its path; since this fact is independent of the collision frequency, the same equation of state applies to both approaches.
A comprehensive theoretical treatment of the linear stability of a sub-Alfvénic plasma expansion ... more A comprehensive theoretical treatment of the linear stability of a sub-Alfvénic plasma expansion is developed. The analysis is similar to those performed for the lower-hybrid-drift instability and the drift cyclotron instability. In addition to the diamagnetic drift (Vdi) that drives these instabilities, the gravitational drift (Vg) caused by the deceleration of the plasma shell, and the Pedersen drift (VP) caused by ion–neutral collisions and neutral gas flow, are included. The emphasis of the paper is on the instability driven by the gravitational drift. The theory is fully kinetic and includes finite-beta effects (i.e., electromagnetic coupling and electron ∇B drift-wave resonances), collisional effects (electron–ion, electron–neutral, and ion–neutral collisions), and neutral gas flow, effects that have not been considered to date. The analysis is carried out in a slab geometry although the applications are to spherical expansions. The main conclusions are as follows. In the stro...
A tokamak plasma rotating poloidally at speeds in excess of the poloidal sound speed is studied. ... more A tokamak plasma rotating poloidally at speeds in excess of the poloidal sound speed is studied. The study is motivated by the propositions that shear in the rotation could suppress turbulence and improve confinement and that the poloidal sound speed is the critical speed to exceed for flow profiles distributed over the entire minor radius. For such rapidly rotating plasma regimes, the Grad-Shafranov equation is examined, the damping rate of the rotation is calculated, particle orbits are investigated, and a heuristic MHD stability study is done. It is found that for rotation speeds exceeding the poloidal sound speed but less than the poloidal Alfven speed no deleterious effects can be expected from the rapid rotation as regards equilibrium or MHD stability. The damping rate of poloidal rotation is shown to fall off over the peak rate, in all collisionality regimes, as up-2. This feature makes more efficacious the external driving of such poloidal flow and allows favourable extrapolation to reactor relevant regimes. Finally, it is shown that the fraction of trapped ions is significantly depleted in this regime, suggesting a reduction in the neoclassical heat transport as well
The convection of a magnetically confined plasma resulting from heat and particle sources is stud... more The convection of a magnetically confined plasma resulting from heat and particle sources is studied. It is assumed that the convection is low-level in that the system stays stable to ideal interchange instabilities. A Z-pinch plasma with asymmetric particle and heat sources is considered. It is found that there is no convection if there are no particle sources, independent of the distribution of the heat sources. Particle sources result in convection which in turn influences heat transport. The central temperature, however, may go up or down in response to this convection, depending on the distribution of the source function.
Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrate... more Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfvén wave, and an initial value code solves the resulting equations. The s−α diagram (magnetic shear versus pressure gradient) of ballooning mode theory is extended to include rotational shear. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (dΩ/dq, where Ω is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and direct stable access to the second stability regime occurs when this frequency is approximately one-quarter to one-half the Alfvén frequency, ωA=VA/qR.
The basic idea of centrifugal confinement is to use centrifugal forces from supersonic rotation t... more The basic idea of centrifugal confinement is to use centrifugal forces from supersonic rotation to augment conventional magnetic confinement. Optimizing this “knob” results in a fusion device that features four advantages: steady state, no disruptions, superior cross-field confinement, and a simpler coil configuration. The idea rests on two prongs: first, centrifugal forces can confine plasmas to desired regions of shaped magnetic fields; second, the accompanying large velocity shear can stabilize even magnetohydrodynamic (MHD) instabilities. A third feature is that the velocity shear also viscously heats the plasma; no auxiliary heating is necessary to reach fusion temperatures. Regarding transport, the velocity shear can also quell microturbulence, leading to fully classical confinement, as there are no neoclassical effects. Classical parallel electron transport then sets the confinement time. These losses are minimized by a large Pastukhov factor resulting from the deep centrifug...
A new instability is proposed to instability which can explain the large-scale explain the observ... more A new instability is proposed to instability which can explain the large-scale explain the observed large-scale structuring of the structuring of the AMPTE magnetotail barium magnetotail AMPTE barium releases. The stability releases. The new instability is obtained by using theory is based on a modified set of MHD equations a set of one-fluid equations that is more which allows for large Larmor radius effects, i.e., appropriate for Pi ~ Rc than the ideal MHD Pi ~ R c which is typical of the AMPTE releases equations. The instability is a fluid mode that (here •i is the ion Larmor radius and R_ is the transverse radius of the cloud). The mo•e is driven by the deceleration of the cloud and the density gradient at the edge of the cloud. The predicted linear growth rate and eigenmode structure are consistent with AMPTE observations.
Recent studies of transient reconnection show presence of dipolarization fronts which are charact... more Recent studies of transient reconnection show presence of dipolarization fronts which are characterized by a steep increase or jump in the z component of the earth's tail magnetic field. This has been reported in satellite data as well as kinetic simulations. One possible interpretation of these jumps is the formation of shocks using the standard MHD Rankine-Hugoniot relations. Furthermore in
The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermon... more The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermonuclear fusion. The device is steady state, there are no disruptions, the loss cone is almost closed, sheared rotation stabilizes magnetohydrodynamic (MHD) instabilities as well as plasma turbulence, and the coil configuration is simple. In this work we examine the effect of rotation on mirror confinement using a full cyclotron orbit code. The full cyclotron simulations give a much more complete description of the particle energy distribution and losses than the use of guiding center equations. Both collisionless loss as a function of rotation and the effect of collisions are investigated. Although the cross field diffusion is classical, we find that the local rotating Maxwellian is increased to higher energy, increasing the fusion rate and also enhancing the radial diffusion. We find a loss channel not envisioned with a guiding center treatment, but a design can be chosen that can satisfy the Lawson criterion for ions. Of course, the rotation has minimal effect on the alpha particle birth distribution, so there is initially loss through the usual loss cone, just as in a mirror with no rotation. However after this loss the alphas slow down on the electrons with little pitch angle scattering until reaching low energy, so over half of the initial alpha energy is transfered to the electrons. The important problem of energy confinement, with losses primarily through the electron channel, is not addressed in this work. We also discuss the use of rotating mirror geometry to produce an ion thruster.
APS Division of Plasma Physics Meeting Abstracts, Nov 1, 1997
The Maryland Centrifugal Torus (MCT) is proposed to test the possibility of using centrifugal for... more The Maryland Centrifugal Torus (MCT) is proposed to test the possibility of using centrifugal forces of rotating plasma as an effective "gravitational" potential to confine plasma along the magnetic field. Thus, the rotation consititutes an additional "knob" to aid magnetic confinement. We consider here the underlying theoretical concerns. The flowing MHD equilibrium is studied. Analytical as well as numerical results are presented: "gravitational" confinement is demonstrated. An MHD stability study is summarized: it is shown that a toroidal magnetic field might be essential to achieve complete stability to convective MHD modes. The critical field required for stability is one of the objectives of the MCT experiment. Preliminary results from a numerical experiment to test the stabilization of MHD modes by the large velocity shear will be presented. The scaling of centrifugally confined plasmas to fusion reactors will be assessed. Neoclassical transport is estimated to show that the Lawson Condition is achievable in principle. The advantages of the system - steady state, disruption-free, superior confiement, and simpler coil system - are discussed in conjunction with the disadvantages - large circulating power, alpha losses, insulating first wall.
Submitted for the APR12 Meeting of The American Physical Society Double adiabatic theory of drive... more Submitted for the APR12 Meeting of The American Physical Society Double adiabatic theory of driven collisionless geodesic acoustic modes (GAMs) in toroids 1 ADIL HASSAM, ROBERT KLEVA, WRICK SEN-GUPTA, University of Maryland-The GAM is an axisymmetric oscillation of a toroidal magnetically confined plasma, resulting from an interplay between poloidal plasma rotation and perpendicular flux tube compression from the B field gradient. The frequency is super-parallel-sonic, ie, ω ∼ (ion thermal speed)/R, greater than the parallel acoustic mode which is lower by a factor of q. Consequently, collisionless geodesic acoustic modes in tokamaks can be described by the Chew-Goldberger-Low double-adiabatic fluid closures. This allows a simpler nonlinear formulation. We use these equations to study driven, collisionless GAMs in tokamaks. The motivation for this study is a proposal by Hallatschek and McKee to drive GAMs on the D3D tokamak at resonance. The drivers in the CGL theory include external magnetic forces to effect flux surface displacements as well as sources to provide modulated non-axisymmetric ion heating. We show that the linear mode frequency from CGL theory agrees with previous kinetic results. Comparisons will be made between different approaches to resonate the mode. Nonlinear effects will be evaluated. Results of a 2D toroidal numerical simulation of driven GAMs are described
Uploads
Papers by Adil Hassam