Ignition threshold for non-Maxwellian plasmas

Hay, Michael J.; Fisch, Nathaniel J.

doi:10.1063/1.4936346

Cited by 16 publications

(13 citation statements)

References 37 publications

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“…Some phenomena occurring in these devices break the symmetry of the Maxwellian distribution function (MDF) such as radio-frequency wave heating, neutral beam injection, ion orbit loss or simply boundary and external conditions (plasma-surface interaction, external magnetic field configuration, etc) (see ). Another phenomenon that is highly relevant to future fusion reactors is the self-heating by alpha particles produced by fusion reactions [14,15]. All these phenomena need to be considered in plasma physics in order to better reproduce the dynamics of current tokamaks and predict the confinement of future fusion reactors because to date, there is no rigorous and efficient theory describing non-Maxwellian distributions (NMDF) at finite collisionality.…”

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confidence: 99%

“…[6][7][8][9][10][11][12][13]). Another phenomenon that is highly relevant to future fusion reactors is the self-heating by alpha particles produced by fusion reactions [14,15]. All these phenomena need to be considered in plasma physics in order to better reproduce the dynamics of current tokamaks and predict the confinement of future fusion reactors because to date, there is no rigorous and efficient theory describing non-Maxwellian distributions (NMDF) at finite collisionality.…”

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confidence: 99%

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Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

Izacard

2016

Physics of Plasmas

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In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account specially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very CPU-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa (KDF), the bi-modal or a new interpreted non-Maxwellian (INMDF) distribution function. The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.The observation of non-equilibrium distribution functions is possible in a large number of areas other than laboratory plasma physics such as in astrophysics plasmas, hydrodynamic fluids and molecular dynamics, atomic physics, condensed matter, chemical reactions and in statistics (see Refs. [1][2][3][4][5]). We focus here on laboratory plasma physics with charged particles in a magnetic field relevant to tokamaks and spherical tokamaks for the purpose of energy production by fusion ener...

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Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

Izacard

2016

Physics of Plasmas

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“…In imagining the future, we should be prepared to apply the paradigms developed here to many different configurations, both for applications other than nuclear fusion, and of course for nuclear fusion, possibly using advanced fuels [109], or under exotic plasma conditions, such as high-density degenerate plasma [110]. The paradigm of producing fusion may itself change, such as through fusion-fission parks, using fusion neutrons to breed nuclear fuel for use in conventional nuclear reactors [111].…”

Section: Discussionmentioning

confidence: 99%

Pushing Particles with Waves: Current Drive and <i>α</i>-Channeling

Fisch

2016

Plasma and Fusion Research

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It can be advantageous to push particles with waves in tokamaks or other magnetic confinement devices, relying on wave-particle resonances to accomplish specific goals. Waves that damp on electrons or ions in toroidal fusion devises can drive currents if the waves are launched with toroidal asymmetry. Theses currents are important for tokamaks, since they operate in the absence of an electric field with curl, enabling steady state operation. The lower hybrid wave and the electron cyclotron wave have been demonstrated to drive significant currents. Noninductive current also stabilizes deleterious tearing modes. Waves can also be used to broker the energy transfer between energetic alpha particles and the background plasma. Alpha particles born through fusion reactions in a tokamak reactor tend to slow down on electrons, but that could take up to hundreds of milliseconds. Before that happens, the energy in these alpha particles can destabilize on collisionless timescales toroidal Alfven modes and other waves, in a way deleterious to energy confinement. However, it has been speculated that this energy might be instead be channeled instead into useful energy, that heats fuel ions or drives current. An important question is the extent to which these effects can be accomplished together.

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“…This created a plasma condition where the Bremsstrahlung radiation loss power density could be reduced while maintaining the fusion power density. 6,17 2. By increasing the proton fraction x p of the plasma ions, reducing the effective charge (Z eff ) of the plasma, the Bremsstrahlung radiation loss would be reduced furthe,r 6,17 without reducing the fusion power substantially.…”

Section: Introductionmentioning

confidence: 99%

Toroidal plasma conditions where the p-11B fusion Lawson criterion could be eased

Peng¹,

Shi²,

Wang³

et al. 2020

Preprint

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We examine the theoretical conditions in which the Lawson ignition criterion for p-11B fusion in a magnetized toroidal plasma can be reduced substantially. It is determined that a velocity differential between the protons and the boron ions of the order of the plasma sound speed (Mach number of 1 or 2 at a plasma temperature of ~102 keV) could raise the p-11B fusion reaction rate to ~2x10-22 m3/s or ~6x10-22 m^3/s, respectively, from the ~1x10-22 m3/s level in a static plasma. The Lawson triple product (ni τE Ti) required for ignition can thereby be reduced to as low as ~1023 m-3 s keV, which is one order of magnitude above the ITER requirement for D-T burn. Since order-unity Mach numbers in velocity differentials between deuterons and impurity carbon ions have been maintained in tokamak plasmas under excellent confinement conditions, similar levels of velocity differentials between protons and minority boron-11 ions could in principle be maintained also. A theoretical possibility of achieving p-11B fusion ignition in a toroidal plasma of ~102 keV in ion temperature is hereby presented. Similar p-13C plasmas, for example, will introduce a possibility of measuring the CNO fusion chain reaction rates in a laboratory.

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Ignition threshold for non-Maxwellian plasmas

Cited by 16 publications

References 37 publications

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

Pushing Particles with Waves: Current Drive and <i>α</i>-Channeling

Toroidal plasma conditions where the p-11B fusion Lawson criterion could be eased

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