Proceedings of ITC/ISHW2007

Time-Dependent NBI-Heating Simulation of LHD Plasmas
with TOTAL (Toroidal Transport Analysis Linkage) CodeT. Ohnishi1), K. Yamazaki1), H. Funaba2), H. Arimoto1), T. Shoji1)
1)

2)

Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan

Abstract. The time-dependent simulation of neutral-beam-heated LHD plasmas has been carriedout using a simulation code TOTAL (Toroidal Transport Analysis Linkage) focusing on the timeevolutions of beam energy and kinetic energy. This code consists of 3-dimensional equilibrium
VMEC with bootstrap currents and a 1-dimensional transport HTRANS with neoclassical loss
determined by ambipolar radial electric field as well as anomalous transport. The neutral beam
deposition is calculated by the Monte Carlo code HFREYA, and the slowing down process wascalculated by the Fast Ion Fokker-Plank code FIFPC. The simulated time evolution of total energy
including beam energy roughly agrees with the time evolution of the experimentally measuredenergy. The temporal change in the beam velocity distribution is also clarified.
Keywords: NBI-heating, LHD, Fokker-Plank equation, velocity distribution function, neoclassicaltransport, anomalous transport

1. Introduction

In order to get high temperature plasmas, neutralbeam injection (NBI) heating plays an important role.
Since plasma is heated due to collision with fast particle
injected by neutral beam injection device, NBI schemeheats both plasma ion and electron efficiently in the future
fusion reactors.
Up to now, the simulation of NBI heating in LHD
experiments usually has been done in steady-state manner,and the time-dependent heating process has not beenclarified in details. In this paper, we focused on thetime-dependent simulation of neutral-beam-heated LHD
plasma; especially, on the time evolution of kinetic energy
and beam energy. In the next section, the simulation model
is described. The simulation results are shown in Section 3,
and the summary is given in the final section.

2. Simulation Model

In order to analyze LHD plasma heated bynegative-NBI heating scheme, we have used Fast Ion
Fokker-Planck Code (FIFPC) [1], which solves theslowing down process of fast ions, HFREYA code, which
computes the deposition of injected neutral particle inhelical plasma, and Toroidal Transport Analysis Linkage(TOTAL)[2, 3] code, which consists of 3-dimensional(3-D) equilibrium/ 1-D transport equations with both
neoclassical transport and anomalous transport.

e-mail: t-ohnishi@ees.nagoya-u.ac.jp

Fig.1 Schematic flow chart of the TOTAL code.
For the analysis of the LHD transport, a 2.0-D
equilibrium-transport code has been developed in which
the 3-D equilibrium code VMEC [4] and the 1-Dtransport code HTRANS are used. The NBI deposition iscalculated by the HFREYA code, which is a helicalmodification of FREYA [5], and the slowing down
calculation is done with the Fokker-Planck codeProceedings of ITC/ISHW2007

2.2. Fokker-Planck equation

We adopt a typical LHD discharge of the shot number
24512 [8](inward shifted configuration with magnetic axis
radius Rax = 3.6m;, magnetic filed strength B0 = 1.5T) to
investigate the NBI-heating process. A tangent injection
beam ion energy, Eb, and beam power Pb are 142.9 keV
and 4.72 MW, respectively. We have used input value ofaverage electron density <ne>sim as shown in Fig.2. This
figure also shows the experimental value <ne>exp and NBIpower.
0 .3#24512

NBI10 .2 560
500 .2

NBI20 .1 540

<ne>

30

<ne>exp0 .1

20100 .0 5
0NBI1,NBI2 [kJ]

To analyze this simulation, we have used FIFPC tosolve the Fokker-Planck equation that describes theslowing down process of fast ions. The FIFPC may be usedalone for treating neutral beam injection problems, or incombination with transport codes which describe theevolution of helical core plasma. The code is designed tocalculate the fast ion distribution function in polar
coordinates in velocity space at time t. The Fokker-Planck
equation which yields the velocity space fast ion
distribution function f(x, θ, t) is

3. Simulation Results-3

The initial vacuum magnetic surface is calculatedby the magnetic tracing code HSD [7] with carefullyarranged multi-filament currents. In the paper, the freeboundary version of VMEC is used. The FCT andBoot-strap currents can be included; these currents are
estimated to be not large enough to affect the present
transport analysis done in this paper. The 3-D magnetic
field obtained by the finite beta equilibrium of VMEC isused to evaluate the NBI heat deposition and themulti-helicity neoclassical ripple transport coefficients.

(3)

where mf and mH are the fast ion mass and the mass ofhydrogen. B, C, D, D1, D2 and E are constant coefficients
given in Ref.[1].

132.1.Equilibrium analysis,<ne> [10 cm ]FIFPC[1]. The anomalous transport is assumed fitted to theglobal experimental scaling laws ISS95 scaling law [6]with some confinement improvement factor. The
schematic flow chart of this simulation code is shown inFig. 1.

00 .5

11 .5

20tim e [s ]Fig.2 Experimental value of average electron density<ne>exp and NBI power NBI1,2 and input value of <ne>.
300’(1)

where the terms on the right-hand side are due to charge
exchange, drag, speed diffusion, angular scattering, theelectric field, compression, and the source of injected fastions, respectively. The plasma major radius, R(t), istime-dependent due to adiabatic compression which is notused here. The Spitzer slowing down time τs and thecharge-exchange lifetime τcx(v) are given by,and(2)Energy [kJ]250

W total
W exp
W plasma

200
150

W beam100
50
000 .511 .5

2t im e [ s ]Fig.3 Time evolution of experimental and simulated
beam/plasma energy in LHD.
The simulation results and typical experimental plasmaenergy data observed by diamagnetic coil measurement areshown in Fig. 3. In the figure, Wtotal is the summation ofProceedings of ITC/ISHW2007
the simulated kinetic plasma energy, Wplasma = 3nk(Te +Ti)/2, and the beam energy, Wbeam. In order to compare
Wexp and Wtotal , we should define Wtotal = Wplasma + fWbeam ,where f ~ 1/5 - 1/3. The profiles of Wexp and Wtotal roughly
agree with each other3 1013

time=1.4 s

1500

2 10131000

1.5 1013
1 1013

Te, Ti [eV]ne [cm-3]

2.5 1013(a) 1.0x10-5 s and (b) 0.4 s. The parallel component andperpendicular component of stored energy is also plotted inFig.5. At 1.0x10-5 s, the stored energy is almost parallelcomponent energy. The perpendicular component is very
low energy. At 0.4 s, the perpendicular energy increases toabout a quarter of parallel energy. The beam energy is
gradually transferred to various angles by diffusion andscattering process. So we investigated the distributionfunction in velocity space in order to analyze the details ofenergy transfer.
-78 10(a) =1.0x10-5-7

7 10500-7

5 10-700.2

0.4

0.6

01

0.8rhof(E)

5 100-7-72 10(a)0-5time=1.0x10 s
stored energy

14

2.5 1000.2 0.4 0.6 0.8
E/E01

1.2 1.4-52 1014

5 10

stored parallel energy

1.5 1014(b) t=0.2

4.6 degree
0.0 degree(beam direction)

-5

4 10

14f(E)

1 10

5 1013

00.2

0.4

0.6

0.8

1

1 10-5time=0.4 s

0rho

17(b)

17

1 10

stored energy0

0.2 0.4 0.6 0.8
E/E01

1.2 1.4(c) t=0.4
4.6 degrees
1.5 100.0 degree-5(beamdirection)
1 106 1016

-5f(E)

4 1016018.5 degree

2 10-5stored parallel energy

8 10162 1016

3 10-5
2 10-5stored perpendicular energy

1.2 10energy

0.0 degree

1 10-714

3 100-7

4 10
3 10Fig.4 The profiles of electron and ion temperature andelectron density at 1.4 s obtained in simulation.

energy4.6 degree(beam direction)

6 1012

Stored perpendicular energy

18.5 degree
00.2

0.4

rho

0.60.8

1Fig.5 profile of stored energy, parallel energy component
and perpendicular energy component in plasma:(a) 1.0x10-5 s; (b) 0.4 s.
The Fig.4 shows electron density, ne, and electron andion temperature, Te and Ti, at 1.4 s. The density profile inthe core is flat up to ρ=0.6. The electron temperature inplasma core is 1.4 keV, and the ion temperature is 0.9 keV.
The Fig.5 shows stored beam energy in the plasma at-65 1000416487 0.4 0.6 0.8
0.2
E/E0.711.2 1.4Fig.6 The distribution function of the beam ions calculated
by Fast Ion Fokker-Planck Code (FIFPC);(a) 1.0x10-5 s, (b) 0.2 s, (c) 0.4
The Fig.6 shows the distribution function in velocity
space at ρ = 0.47. The figures (a), (b) and (c) are profiles ofProceedings of ITC/ISHW2007
the distribution function at 1.0x10-5 s, 0.2 s and 0.4 s
respectively. At 1.0x10-5 s, there are many ions of highenergy at E/E0=1. The beam energy is gradually transferred
to high angles.
We can see from Figs. 5 and 6 that the beam consists
only from the well circulating particles, and the mostenergetic ions are located in the plasma core.
In the code, particle orbit effects can be included bybounce average orbit in the heating process, however, thiseffect is not evaluated in the present simulation, because
the present discharge analyzed here is the medium field,
low beta operation. In the lower magnetic field and higher
beta plasma case, this effect should be included.

4. Summary
We analyzed NBI-heating time-dependent processwith TOTAL code. The stored energy is almost parallel
component directly after injection. Later, the energy isgradually transferred to perpendicular component bydiffusion and scattering process. In order to analyze thevelocity distribution in detail, we used Fast Ion
Fokker-Planck Code (FIFPC), which solves the FokkerPlanck equation. Directly after injection, there are manyions of high energy at E/E0=1. Later, the high energy ion is
gradually transferred to plasma core direction.
We can conclude from here that (i) the beam consists
only from the well circulating particles, and (ii) the mostenergetic ions are located in the plasma core; there, thebeam can hardly lead to edge-localized instabilities.
In summary, the time evolution of simulated totalenergy including beam energy roughly agrees with that of
the experimentally measured energy. The temporalchange in the beam velocity distribution is also clarified.

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