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ICRF Fast Wave Heating and Current Drive on KSTAR Plasma

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ICRF Fast Wave Heating and Current Drive on KSTAR Plasma KR9800092 KAERI/TR- ICRF Fast Wave Heating and Current Drive on KSTAR Plasma 1997 29-16 £ fijl-Mf- ICRF Fast Wave Heating and Current Drive on KSTAR Plasma 1997 V! 7 € , Post Doc.) , Post Doc.) ABSTRACT For the efficient plasma heating and current drive, the structure of ICRF fast wave propagation and absorption in a tokamak plasma should be first investigated. Several operating scenarios for ICRF fast wave heating and current drive have been explored over a fairly large range of density and temperature on KSTAR [Korea Superconducting Tokamak Advanced Research] [1]. Numerical calculations have been performed using the global wave code, TORIC [2]. The code TORIC solves the finite Larmor radius wave equations in the ion cyclotron frequency range in an arbitrary axisymmetric toroidal geometry. The fast wave propagation/absorption characteristics, power partitions among plasma species and the driven current/current drive efficiencies are calculated. ^l- ifloflA) KSTAR ^?W £ TORIC Contents Abstract List of Tables List of Figures 1. Introduction 1 2. Overview of Heating and Current Drive Scenarios on KSTAR 2 3. Model Equations 3 3.1 Wave Equation 3 3.2 Magnetic Equilibrium 4 3.3 Power Balance 5 3.4 FWCD Modeling 6 4. ICRF Fast Wave Heating 6 5. FWCD 8 6. Summary 9 Acknowledgements 10 References 10 List of Tables Table. 1 The Reference KSTAR Parameters Table. 2 TPower Partitions of Plasma Species List of Figures Fig. 1 Variation of cyclotron resonance frequency of various ion species across the plasma minor radius Fig. 2 The flux-Surface Averaged Power Deposition Profile .vs. p Fig. 3 2-D Contour of Fast Wave Electric Field (EJ in the (R,Z) plane Fig. 4 Absorbed Power spectrum .vs. the toroidal mode number Fig. 5 Power Partitions .vs. the toroidal mode number Fig. 6 Absorbed Power spectrum .vs. the toroidal mode number Fig. 7 Driven Currents as a function of ne(0), for P=6MW at 38 MHz with K/2 inter-strap phasing Fig. 8 The flux-Surface Averaged Power Deposition Profile .vs. p Fig. 9 The flux-Surface Averaged Driven Current Profile .vs. p 1. Introduction One of the KSTAR research objectives is to explore the methods to achieve a steady state operation using non-inductive current drive for tokamak fusion reactors. Heating and current drive are one of the main features in the operation of reversed shear plasma on KSTAR. A magnetized plasma allows the variety of wave modes, and thus the corresponding different radio frequency schemes are available. The KSTAR plasma heating relies on the fast magnetosonic wave in the ion cyclotron range of frequency. Fast wave propagating into the plasma deposits its energy at a localized absorption zone inside the plasma through the second harmonic resonance in a single ion species plasma, or the fundamental harmonic resonance of minority ions in two ion species plasma. The accessibility to the resonance zone and damping mechanism of fast waves can be investigated from the cold or warm plasma dispersion models. The fast wave can be used to drive the current required for the steady state oper- ation of a tokamak or to modify the driven current profile for the better confinement. Current drive is achieved by the direct absorption of waves by electrons under elec- tron Landau damping (ELD) and transit time magnetic pumping (TTMP). For efficient current drive, the frequency must be chosen such that the parasitic absorp- tion by ions through the ion harmonic resonances can be minimized. In general, the wave absorption by electrons increases with the frequency. However, at higher fre- quency, it becomes increasingly difficult to avoid ion harmonic resonances since they are increasingly closely spaced, while at low frequency, it is relatively low. Thus the lower single pass absorption due to multi-pass of the weakly absorbed wave results in the lower current drive efficiency. The code TORIC solves the finite Larmor radius (FLR) wave equations in the ion cyclotron frequency range in an arbitrary axisymmetric toroidal geometry with the analytically described equilibrium. These finite Larmor terms have very important effects on the ions resonant near the second harmonic resonance of ions. The wave model implemented discribs the fast wave, Alfven wave and ion Bernstein wave excited by mode conversion near the second harmonic resonance layer. The effect of 1 toroidicity on the parallel dispersion, giving appreciable broading of the cyclotron resonance region, is taken into account. The way in which the parallel component of the electric field is evaluated improves the accuracy of power absorption by the electrons, and gives a more reliable evaluation of the current drive efficiency in the IC frequency range. For the numerical resolution of ion Bernstein waves with a very short wavelength, ion Bernstein waves are damped when their wavelength becomes with the ion Larmor radius. In section 2, the different operating scenarios that will be used for ICRF fast wave heating and current drive on KSTAR are overviewed. The wave equations and numerical algorithm implemented into the code TORIC for the calculations of driven current and CD efficiency are summarized in section 3. In sections 4 and 5, the numerical results on the proposed KSTAR operating scenarios are presented using the global wave code, TORIC [2], over a fairly large range of density and temperature. 2. Overview of Heating and Current Drive Scenarios on KSTAR The reference KSTAR plasma and antenna parameters are given in Table 1. With #o=3.5T, Fig. 1 shows the variation of cyclotron resonance frequency of vari- ous ion species across the plasma minor radius and the wave frequency range of the proposed operating modes. Three operating scenarios for the heating and current drive have been studied for KSTAR: 1. H minority heating in D majority plasma. The frequency of 50 MHz is good for H minority heating or second harmonic heating of D. 2. Current drive in D majority plasma with H minority. The frequency of 38 MHz can be used as the low frequency operation scenario for FWCD. 3. Current drive in H-only plasma. Operation at 75 MHz may be possible for high frequency FWCD in H-only plasma, depending on the RF circuit design. To cover these proposed operating frequency ranges, RF transmitters must be op- erated over 30 to 80 MHz frequency range. 3, Model Equations 3.1. Wave Equation TORIC solves the Maxwell wave equation given by: VxVx E = ^(E + ^(^ + J^)) (1) where jr is the plasma current and JA the antenna current. In FLR approximation, the plasma current can be approximated by J * J» + J2 ji2) + jt*> (2) tons where j(°\ J} ' and Jj2) denote the zero Larmor radius current, the ion and electron FLR currents, respectively. The vector forms of FLR plasma currents contain the orbit integral operators along the magnetic field lines. The TORIC evaluates these parallel orbit integral operators analytically using the toroidal plasma dispersion function of Z(x). Finally the FLR currents are described by the following algebraic operators [2]: L = 1 - £ ^4 (<f " **Z(*K)) (3) uL Elf () (5) where xn,a = xn>a(m, TP, tf) = —— (6) K£ vth,a The toroidal plasma dispersion function of Z(x) taking into account the toroidal broading of the cyclotron resonances is approximated in terms of the ordinary plasma dispersion function Z(x) with the argument evaluated using an appropriate effective parallel wave numbers: - x0Z{xn) * -x0Z(xn) (7) 2 1 r+oo e-u x Z(xn) = -p / du + i^e- " (8) yJIT J-oo U — Xn where which is evaluated at the cyclotron resonance. The important effect of toroidicity is expressed through the 7, which means the appreciable broading the cyclotron resonance region. 3.2. Magnetic Equilibrium TORIC represents the axisymmetric MHD equilibrium of the form [2]: ) X (T/>,T9) = A(^/>) + aip cos^fl — 5(V ) sin$) (12) Z (tp,d) = a,T)(xf}) sin tf (13) B = BoRo(a /(^)V ip x V ij> + g(ip) V <p) (14) = —=-BQ (sin 9 tT + cos 9 e^ ) (15) R where fan tf = |^ = a ^fjf}. The functions A(^) (Shafranov shift), (ellipticity) and 8(ip) (triangularity), as well as f(ip) and g(ip) should be specified consistantly with MHD equilibrium conditions. However, the current version of TORIC used for KSTAR simulation study uses the simple analytic formula for the description of equilibrium: 2 A(V>) = Ao( 1 - V ) (16) «W = <$o ^ (17) 2 ^) = [e0 + (e, - eo)V> ] i> (18) Here, So is the Shafranov shift of the magnetic axis, and e0 t\ the ellipticity at the magnetic axis and the plasma edge, respectively. The dependence of R B^ on T/> is neglected, i.e. g(ip)=l. f(i>) is given by = a dSv (20) is the total toroidal current inside the magnetic surface tp, which ensures that the equilibrium conditions are satisfied at least on average on each magnetic surface. 3.3. Power Balance The global power balance is given by 2 Paba = P°J3 + P Ja + PlCa (21) where Pa£a and Pa(|* is the power absorbed by iones at the fundamental and second e harmonic ion cyclotron resonances, respectively, while P^ a is the power absorbed by electrons, which includes both the electron Landau damping (ELD) and Transit time magnetic damping (TTMP). The explicit discriptions for each Pab3 are given in Ref. [2] in more detail. Assuming the perpectly conducting wall and no absorption between the antenna and the wall, the total absorbed power by plasma species must be equal to the power radiated by antenna and the electromagnetic power flux across the magnetic surface toward the plasma center tp = tpA, given by. PA = 1 j Re[E*(r) • JA(r)}dV = J PabsdV (22) where PA is the power radiated by the antenna and JA is the current in the antenna.
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