Electron Cyclotron Resonance Heating of Plasma (in H-1)

Electron Cyclotron Resonance Heating of Plasma in H-1

M.G. Shats

Plasma Research Laboratory

Research School of Physical Sciences and Engineering

The Australian National University

Canberra

Michael.Shats@anu.edu.au

Outline

Introduction

Attractiveness of the method

Wave propagation and absorption

Microwave technology

Options for H-1

Power transmission and launching

ECRH Modelling

Physics studies using ECRH

What we can expect

Introduction

Electron-cyclotron resonance heating (ECRH) project

has started in collaboration with NIFS (Nagoya, Japan) and IAE (Kyoto University) based on the loan of 200 kW 28 GHz gyrotron and a power supply from Japan.

Attractiveness of the method

ECRH has proven itself to be the most successful way of plasma production and heating in other stellarators due to its experimental flexibility.

During the ECRH, the microwave power is directly transfered to electrons increasing thus the electron temperature of plasma in the region defined by the crossing of the ECR layer with the millimeter-wave beam.

Depending on the plasma parameters (magnetic field, electron temperature and density), the choice of the electron cyclotron harmonic and the polarization of the wave, the single-pass absorption of the power can reach almost 100%.

The need in the ECRH in H-1 heliac is dictated by a number of unique features possesed by this plasma production and heating technique.

Physics advantages

Localized power deposition

Launching of a well collimated microwave beam with a controlled direction and polarization.

High electron temperature achievable

Technology advantages

antenna can be located far from the plasma, thus avoiding impurity release from antenna;

compactness of the antenna design;

high efficiency of the power transportation and coupling to plasma.

Wave propagation and absorption

DISPERSION RELATION

(see M. Bornatici et al. Nucl. Fusion,23 (1983)1153)

Maxwell equations

collisionless Boltzmann equation

In homogeneous magnetized plasma:

Dispersion tensor:

, det(L) = 0,

where , (i,j = x,y,z)

d_ij unit tensor, N = ck/w refractive index

Refraction effects are described by the cold plasma dispersion relation.

Dielectric tensor (cold plasma)

where and .

Two solutions ("-" O-mode, "+" X-mode):

where

The most practically important (for heating) case is perpendicular propagation:

Two types of waves:

Ordinary Mode (O-mode):

Linearly Polarized

Propagates as long as w > w_pe

(like in unmagnetized case)

Extraordinary Mode (X-mode):

Elliptically polarized (E_k due to fluct. space charge)

Has 2 propagation limits

low- and high-density cut-offs:

Collective resonance at Upper Hybrid frequency:

Cut-offs and resonances for perpendicular launch of the first-harmonic O- and X-mode in tokamak-like configuration with parabolic density profile

(n_e(0) > cut-off density)

Approach to inhomogeneous plasma

Geometrical optics (WKB) approximation

l << L, 2p/w << T

Wave electric field is described by Eikonal approximation:

where S(r) is the wave phase (eikonal) and e_n is a position.

Constant S surfaces are called geometrical wave fronts.

A ray path is defined as trajectory orthogonal to the geometrical wave fronts and is described by the Hamiltonian formalism:

where D(r,k,w) = det {Re[L(r,k,w)]}

(L is a local dispersion tensor)

Reflection point coincides with the cut-off point only for a ray propagating along the density gradient

Wave Absorption

Qualitative picture:

1. Parallel propagation (k || B) (X-mode)

[A.G. Litvak et al. Nucl. Fus.17 (1977) 659]

Resonant electrons are directly accelerated in circularly polarized wave, incrementing their perpendicular energy

2. O-mode:

F_Le component of the Lorentz force is resonant with the electron gyration. Increases electron perpendicular energy. [E.V. Suvorov, M.D. Tokman, Plasma Physics, 25 (1983) 723]

Absorption: General Approach

Warm plasma dielectric tensor:

S_ij is a Hermitian tensor (function of electron distribution function), , n is a harmonic number.

The wave absorption is defined by the anti-Hermitian part of the dielectric tensor:

d is Dirac function.

The absorption coefficient a is calculated from the energy balance equation as a function of , the wave electric field and the energy flux S:

, where the energy flux

Importance of relativistic effects

Relativistic effects are important even if

. The resonance condition

where

Doppler broadening of the resonance:

prevails when

(quasi-perpendicular propagation)

Relativistic line width

important when

(oblique propagation)

Energy flux follows the path of the ray and the wave power exponentially decreases along the ray with the rate of a(s):

where a is absorption coefficient

The optical depth t of the plasma

Spatial line width (absorption length)in the inhomogeneous magnetic field:

where for perpendicular propagation the line width is defined by the relativistic effect:

Absorption coefficients for O- and X- modes

O-mode

a

c_n

n=1

n=2

X-mode

n=1

n=2

´

Launching conditions in H-1

mode

launching

density

absorption

comments

n = 1 (B = 1T)

O-mode

LFS

HFS

0 - n_c

good

simple

impossible

X-mode

LFS

HFS

0 - 2 n_c

none

very good

reflection at w₊

impossible

n = 2 (B = 0.5T)

O-mode	LFS HFS	0 - n_c 0 - n_c	bad bad	useless useless
X-mode	LFS HFS	0 - 1/2n_c 0 - 1/2n_c 3/4-3/2n_c	good good good	Low n, low B impossible impossible

Absorbed power in H-1 vs T_e

(n(0)=2´ 10¹²cm^-3)

Physics studies in ECRH plasmas

Transport studies in collisionless plasma

Realistic: n_e £ 10¹³cm^-3, T_e » 1 keV, B =1 T

a) Particle orbit effects

- biased limiters

- trapped particle control

b) L-H transition

combined ICRH+ECRH to manipulate radial electric field

c) Estimate of heat transport coefficients

+ Neoclassical theory prediction

requires detailed power balance

2. Divertor studies

interest from both stellarator and tokamak communities ( ITER, LID on LHD)
Plasma« material interaction

only ECRH can provide localized power deposition necessary for these studies

3. Finite b effects - requires high P_heat

4. Fluctuations and turbulence

ECRH is ideally suited for a variety of plasma physics experiments in H-1:

- production of high electron temperature plasma in low-collissionality regime;

- electron temperature profile shaping;

- heat-wave propagation experiments to measure local thermal conductivity of plasma;

- transport studies, including the effects of magnetic islands and island divertor configurations.

At the first stage, ECRH experiment in H-1 will be performed at the second cyclotron harmonic (magnetic field will be 0.5 T) with an extraordinary mode (electric vector of the heating wave is perpendicular to the magnetic field of the machine) launched from a low magnetic field side. Since the single-pass absorption of the power at low densities is not expected to be higher than 20 to 30%, the unabsorbed power will be collected and focussed back into the plasma providing thus higher heating efficiency. An estimate of the plasma parameters achievable with a single gyrotron (based on other stellarator experiments) gives the density above 10^18 m^-3 and the electron temperature in the range of 400 to 800 eV which is more than an order of magnitude higher than at present.

A second stage of ECRH experiment will be a fundamental electron cyclotron harmonic heating with an ordinary mode (electric vector of the heating wave is parallel to the magnetic field of the machine) at the magnetic field of 1 T. This will allow to increase the plasma density by a factor of two and to improve plasma confinement.

A development of the quasi-optical transmission line is under way in collaboration with physicists from Japan. The design relies on the transformation of the output gyrotron mode into a Gaussian beam which is then transported to plasma by a combination of quasi-optical mirrors and corrugated waveguides. Total losses of the microwave power are expected to be lower than 20%.

The construction and test stage of the project is planned for the first half of 1998 with first plasma experiments later in the year.

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