Modeling of HHFW Heating and Current Drive on NSTX with Ray Tracing and Adjoint Techniques

In recent HHFW current drive experiments on NSTX, relative phase shift of the antenna array was scanned from 30 deg. to 90 deg. to create k parallel spectral peaks between 3 and 8 m-1, for rf power in the 1.1-4.5 MW range. Typical plasma parameters were Ip ∼ 0.5 MA, BT ∼ 0.45 T, and neo ∼ 0.6-3x1019 m-3, and Teo ∼ 0.6-3 keV. In this paper, detailed results from the CURRAY ray tracing code at various time slices of some of the earlier discharges are presented. The complete antenna spectrum is modeled using up to 100 rays with different kφ, and kθ. The rf-driven current is calculated by invoking the adjoint technique that is applicable to toroidal plasmas of all aspect ratios and beta values. In these low β (∼2-3%) discharges, the rf-driven current is peaked on axis and minority ion absorption displays a tendency to increase at lower k parallel. Reasonable agreement with inferred results from the voltage measurements has been obtained that points to evidence of current drive, while the calculated power deposition profiles agree very well with the HPRT ray code for these discharges. The use of the adjoint method will become more important in future high β NSTX discharges