The distribution of ion orbit loss fluxes of ions and energy from the plasma edge across the last closed flux surface into the scrape-off layer

Abstract

A more detailed calculation strategy for the evaluation of ion orbit loss of thermalized plasma ions in the edge of tokamaks is presented. In both this and previous papers, the direct loss of particles from internal flux surfaces is calculated from the conservation of canonical angular momentum, energy, and magnetic moment. The previous result that almost all of the ion energy and particle fluxes crossing the last closed flux surface are in the form of ion orbit fluxes is confirmed, and the new result that the distributions of these fluxes crossing the last closed flux surface into the scrape-off layer are very strongly peaked about the outboard midplane is demonstrated. Previous results of a preferential loss of counter current particles leading to a co-current intrinsic rotation peaking just inside of the last closed flux surface are confirmed. Various physical details are discussed. V C 2015 AIP Publishing LLC.

Recent Developments in Plasma Edge Theory

“…8 Ion orbit loss, intrinsic rotation and X-transport 8.1 Basic ion orbit loss calculation [19,20] The basic ion orbit loss calculation is of the minimum energy an ion located at a particular poloidal position (ψ 0 , θ 0 ) on an internal flux surface ψ 0 with a direction cosine ζ 0 relative to the toroidal magnetic field direction must have in order to be able to execute an orbit that will cross the separatrix at location (ψ sep , θ sep ). We use the conservation of canonical toroidal angular momentum…”

“…In the GTEDGE code (a background modeling and experimental data interpretation code), this equation is solved many times for each of 8 values of θ s , 8 values of θ 0 , 22 values of ζ 0 over -1< ζ 0 <1 and 24 values of ρ 0 , using experimental radial electric field and ion temperature gradients in order to generate the minimum physically realistic value of E min (ζ 0 , ρ 0 , θ 0 , θ s ) = 1/2mV 2 0min (ζ 0 , ρ 0 , θ 0 , θ s ) as input for the IOL numerical computational strategy [20], which takes into account that ions could spiral about the flux surface many times in the time required to be transported radially to the next flux surface in determining the ion orbit loss. Once the minimum loss energy E min (ρ 0 , ζ 0 ) for ions on internal surface ρ 0 with direction cosine ζ 0 is determined by one of the computational strategies [19,20], the cumulative loss fraction that has taken place over 0 < ρ < ρ 0 of the total ion population with directions cosine ζ 0 that would have been present in the absence of IOL can be calculated from…”

“…4, the fraction of ions and ion energy leaving the plasma on loss orbits is large in the edge. These lost ions and ion energy are deposited primarily in the SOL near the outboard midplane [20]. Fig.…”

“…8.2 Intrinsic rotation [17,19,20,20,21] The preferential loss of counter-current ions leaves the edge plasma with a predominant co-current ion population, the net current resulting from which can be calculated from…”

Inclusion of ion orbit loss and intrinsic rotation in plasma fluid rotation theory

“…A methodology previously has been developed for calculation of the ion-orbit-loss of particles, momentum, and energy in the thermalized outflowing ion distribution in tokamak edge plasmas. 1,2 The calculation is based on combining the requirements for the conservation of canonical angular momentum, energy, and magnetic moment to obtain an equation for the minimum speed a particle at a given location ðr; hÞ on an internal flux surface with a given pitch angle f 0 (with respect to B) must have in order to reach a given location on the last closed flux surface (LCFS), V 0min ðf 0 Þ. This minimum V 0min ðf 0 Þ enables the calculation of the fractions of particles, ion energy, and ion momentum flowing across an internal flux surface in the edge plasma that consists of free-streaming ion-orbit-loss particles.…”