A microwave beam is launched from the inboard side of a tokamak along the midplane

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Cold magnetised plasma waves: the dielectric tensor, cutoffs, resonances and the CMA diagram

Problem

170\,\mathrm{GHz}

microwave beam is launched from the inboard side of a tokamak along the midplane, travelling outward through the magnetic axis in the extraordinary (X) polarisation. Position

x

is measured from the magnetic axis, positive outboard; the field is

B(x) = B_0R_0/(R_0+x)

with

B_0=5.3\,\mathrm{T}

x=0

and

R_0=6.2\,\mathrm{m}

, and the density profile is the parabola

n_e(x) = 1.0\times10^{20}(1-x^2/a^2)\,\mathrm{m^{-3}}

with

a=2.0\,\mathrm{m}

. At

x=0

this density and field give

X=0.28

. The beam enters at the inboard edge

x=-2.0\,\mathrm{m}

. ((a)) Calculate

Y=|\Omega_e|/\omega

at the inboard edge and state whether it is above or below

Y=1

, the electron cyclotron layer. ((b)) Explain why, moving inward from

x=-2.0\,\mathrm{m}

, the beam cannot meet the X-mode cutoff

R=0

(which needs

X=1-Y

) before

Y

falls to

1

. ((c)) Find the position

x

at which

Y=1

and the value of

X

there. Evaluate the X-mode index

n^2=RL/S

at that layer, and find the first X-mode cutoff or resonance the beam meets beyond it, and where.

Browse the problem library