Hotter Electron Mode of Operation Established with High Power Electron Landau Heating in HL2A

1
Hotter Electron Mode of Operation Established
with High Power Electron Landau Heating in
HL-2A   Gao Qingdi Southwestern Institute of
Physics, P.O.BOX 432, Chengdu 610041, P R China
2

• 1 Introduction
• In order to elevate the plasma parameters and
  achieve more interesting operation scenarios in
  HL-2A as early as possible, a campaign to carry
  out plasma heating using the available auxiliary
  heating schemes is essential.
• Now the available auxiliary heating schemes
  include
• LH wave 4-5 klystrons with power up to 2.5 MW
  at frequency f2.45GHz
• NBI one beam line with power P ? 0.8 MW at
  energy E ? 20 keV
• They had been successfully used in the HL-1M
  tokamak.

3

• To study the electron transport specifically,
  particularly good conditions are provided by
  using preferentially dominant electron heating at
  low density. It can be provided by lower hybrid
  heating (LHH) and current drive (LHCD).
•  
• To know the prospective operation scenario upon
  injection of high power LH wave in HL-2A, the
  effectiveness of plasma heating by electron
  Landau interaction in the lower hybrid range of
  frequency is investigated.
•  
• Some preliminary simulation results are
  presented that include preferentially dominant
  electron heating by LHH at low plasma density,
  and enhanced ion heating during combined NBI and
  LHH.

4
2 LH wave propagation and absorption It is
assumed that the wave electric field can be
decomposed into a set of components (WKB
approximation is valid),

Suppressing the index j, each mode locally
satisfies the wave matrix equation
For a non-trivial solution,
5
To proceed, it is convenient to choose a local
Cartesian system such that
For LH waves, the electron cyclotron frequency is
much higher than the wave frequency, which is
much higher than the ion cyclotron
frequency which is assumed throughout. In the
Hermitian part of the dielectric tensor we keep
only cold plasma terms, except that the dominant
warm plasma term is carried to guard against
singularity near the lower hybrid resonance. The
anti-Hermitian part of the tensor is retained as
a perturbation. For the case at hand, the
principal such term enters as an imaginary
correction to Kzz, and describes the interaction
between the component of the wave electric field
parallel to B and electrons whose speed along B
matches that of the wave (Landau damping). Thus
the plasma dielectric behavior is described by
the following tensor elements

6
(No Transcript)
7
The thermal term designated by ? would be
important near lower hybrid resonance. The
wave-particle interaction responsible for
electron heating and current drive is in Kzz,i.
In the event, the lower hybrid resonance should
become important, a thermal term representing the
ion wave-particle interaction would have to be
added to Kxx and Kyy, but here we assume such
terms vanish. In the Cartesian co-ordinate
system, we decompose the dispersion relation into
its real and imaginary parts,
D Dr iDi 0, where
8
The extension of the local solutions to spatially
inhomogeneous plasma is accomplished by the
eikonal method, with the useful result that an
initial wave field at r with an initial
propagation vector k evolves according to
Hamiltonian equations which preserve the local
dispersion relation Dr 0 along the ray
trajectories
As in Hamiltonian mechanics, the spatial
coordinates denoted by r are canonically
conjugate to the wave-number coordinates denoted
by k. In the study of the axisymmetric tokamak,
it is the cylindrical coordinate system that the
most natural. In the cylindrical frame one has
(R, Z, ?) and (kR ,kZ, n), where R and Z have
dimensions of length, kR and kZ have dimensions
of inverse length and n is the dimensionless
toroidal mode number. The canonical momentum n is
constant along the ray path.
9
A spectral component of power W experiences a
change ?W over time interval ??
Given the velocity distribution and the profiles
of macroscopic plasma parameters, the absorption
of a lower hybrid spectrum can be computed. An
actual incident wave spectrum is a continuous
function of the parallel wave number. This
continuous spectrum is approximated by assigning
the input power to a number of discrete rays,
each ray having a definite initial k// and
launched power.
10
3 Fokker-Planck analysis
Kinetic equation An electron kinetic
equation can be written as
The wave diffusion operator is the 1-D divergence
of the RF induced flux

where Dql is the quasi-linear diffusion
coefficient, and here it signifies a sum over all
waves in existence on a flux surface, with the
appropriate powers and velocities. A simple sum
is used, which means that we assume there are no
interference effects.
11
We employ a 1-D collision operator as given by
Valeo and Eder,
with the collisional diffusion and drag
coefficient given by
In solving for fe we set ,
because the time for equilibration between RF
power and the electron distribution is short
compared with the time for plasma to evolve. Then
the solution for fe is an integral in velocity
space,
12
Quasi-linear diffusion coefficient An
incremental contribution to the quasi-linear
diffusion coefficient Dql at velocity v// from a
wave field of wave-number k// is given by
where E// represents the amplitude of the wave
field parallel to the static magnetic field. One
instructive way to find the relationship between
field E// and wave power W is to equate Pql, the
energy per unit time per unit volume going into
electrons and out of the wave from the quasi-
linear point of view,
13
with the similar quantity from the ray point of
view, obtaining the incremental Dql from a wave
of power W traversing a flux shell of volume ?V
in time ??.
14
4 Simulation of lower hybrid heating in HL-2A 
Preferentially dominant electron heating

• Plasma current Ip 265kA (deuterium discharge)
• Toroidal magnetic field BT 2.0T
• Line averaged electron density
• Injected LH wave power PLH 2.0MW

15
Fig. 1 Plasma current waveform
Fig. 2 Magnetic geometry of the discharge
16
Fig. 3 Plasma temperatures, Te (full line) and Ti
(dotted line), during LHH. The thin lines show
the plasma temperature without auxiliary heating
(Ohmic heating only)
17
Fig. 4 Electron temperature Te before LHH (full
line), and 10ms (dotted line), 30ms (dash dotted
line), 60ms (dashed line) after LHH.
18

• Enhanced ion heating by LH wave injection during
  NBI heating
• D neutral beam (co-injection), Power PLH 0.5MW,
  Energy E 20keV

Fig. 5 Plasma temperatures, Ti (full lines) and
Te (dotted lines), during combined NBI and LHH.
The thin lines show the plasma temperatures
during NBI only.
19
Fig. 6 NBI power density for beam heating ions
(thick lines), beam heating electrons (moderate
thick lines), and fast ion thermalization (thin
lines) during NBI LHH, and NBI only.
20

• Conclusion
• The electron Landau heating by RF wave in the
  lower hybrid range is investigated. It looks
  promising to establish more interesting operation
  scenarios in HL-2A with the available auxiliary
  heating schemes, which include LH wave and NBI.