Alcator

C-M

od

Advan

cedFull-W

aveSim

ulation

sof

Mode

Con

version

Electron

Heatin

gan

dC

urren

tD

rivein

Alcator

C-M

od

P.T.B

onoli,R

.L.B

oivin,J.A

.G

oetz,W.D

.Lee

E.N

elson-Melby,M

.Porkolab,

S.J.W

ukitch

MIT

PSF

C,C

ambridge,

MA

02139

MB

rambilla

Max

Planck

Institutfur

Plasm

aphysik,G

arching

C.K

.P

hillipsand

G.Schilling

PP

PL,P

rinceton,NJ

08543

Outline of Talk

• Review model calculation:

⇒ Convergence criterion for spectral method to resolve ion Bernstein

waves (IBW).

• Large poloidal mode number simulations of D(3He) mode conversion

electron heating in Alcator C-Mod.

⇒ Poloidal mode number scan.

⇒ Comparison with 1-D model predictions.

⇒ Comparison with experimental data.

• Model predictions for mode conversion current drive in C-Mod.

TORIC Predictions Obtained with Nm = 15 Disagree

With Alcator C-Mod Data for IBW Electron Absorption

Full-Wave Toroidal ICRF Model

• Toroidal Code TORIC (M. Brambilla) employs a spectral expansion

for ~E(x, t) of the form:

~E =∑

m,nφ

~Em,nφ

(r) exp(imθ + inφφ)

◦ Code solves explicitly for fast wave and mode converted IBW electric

field:

◦ Typically Nr ' 240 − 480 (radial elements).

◦ Require −7 <∼ m <∼ 7 to resolve fast wave.

◦ Carry out large poloidal mode simulations using Nr = 240 and

−80 <∼ m <∼ + 80 to resolve IBW.

Convergence of Poloidal Mode Expansion

• Must retain enough modes in m-expansion to resolve shortest λ⊥ in

plasma =⇒ Mode converted IBW.

• IBW propagation characterized by k⊥ρi ' 1. Using k⊥ ∼ (m/r) this

becomes:

m ∼ rρ−1i

◦ For Ti ∼ 2 keV, B0 ∼ 8 T → ρD ∼ 0.08 cm.

◦ For r ∼ rmc ∼ 10 cm, the maximum number of modes needed is

typically Nm = 2mmax + 1 where, mmax ' 125.

Full-Wave 1-D ICRF Model

• 1-D METS Code [D.N. Smithe et al, Radio Frequency Power in Plas-

mas, AIP Conf. Proc. 403 (1997) p. 367.]:

◦ Solves 1-D integral wave equation for ~E(x).

◦ Integral dielectric tensor K(x, kx) evaluated using full Bessel func-

tion expansion.

◦ Accurate to all orders in k⊥ρi.

• Electron Landau damping of IBW at arbitrary k⊥ρi is automatically

included in this analysis.

Single Pass Damping Predicted by METS

B0 ' 7.9 T, f0 = 80 MHz, ne(0) ' 2.3 × 1020 m−3

• Significant electron damping predicted for n3He/ne > 10%.

E+ Solution vs. Poloidal Mode Number (Nm)

B0 = 7.88 T, n3He/ne = 0.30, ne = 2.4 × 1020 m−3, nφ = 10

Nm = 15 Nm = 63 Nm = 161

Increasing Nm Suppresses Off-Axis 3He Cyclotron Damping

B0 = 7.88 T, n3He/ne = 0.30, ne = 2.4 × 1020 m−3, nφ = 10

Increasing Nm Broadens the IBW Absorption Profile

B0 = 7.88 T, n3He/ne = 0.30, ne = 2.4 × 1020 m−3, nφ = 10

TORIC Predictions Obtained with Nm = 161 Agree

Much Better with C-Mod Data for IBW Absorption

Driven Current due to Mode Converted Ion Bernstein Wave

Jrf(ψ, θi) =∑

m

Gmrf (ψ, θi)

∑

m′Sm,m′

IBW (ψ, θi),

Gmrf (ψ, θi) = Grf(v‖ = ω/k‖, ε = r/R)

Gmrf (ψ, θi) computed from adjoint solution of Fokker Planck equa-

tion.

Sm,m′IBW (ψ, θi) computed by TORIC.

TORIC / Adjoint Code Predictions for MCCD in C-Mod (Nm = 161)

B0 = 5.5 T, f0 = 60 MHz, ne(0) = 2.0 × 1020 m−3

n3He/ne = 0.15, Te(0) = 3.5 keV

ηCD ' 0.031 (1020 A/W/m2)

Irf ' 88 kA, Ip = 800 kA

ηRFeld = 0.61, PCD = 3 MW

Summary

• Mode converted ion Bernstein waves at k⊥ρi<∼ 1 have been resolved for

the first time in toroidal geometry using a spectral expansion technique:

◦ Wave solutions obtained for Nm>∼ 161 exhibit convergent behavior.

◦ Simulations with Nm ' 200 − 250 are required to obtain fully con-verged wavefields.

• Resulting predictions for mode conversion electron heating in AlcatorC-Mod are then in much better agreement with experimental data.

• High-m spectral simulations of mode conversion current drive in C-Modhave also been carried out:

◦ Predicted current drive figure of merit (ηCD ' 0.031) results in' 90 kA of driven current with 3 MW of injected fast wave power.