The Columbia Non-neutral Torus (CNT) is now a neutral microwave-heated stellarator (2.45GHZ, 1kW magnetron)
If you have a spare 10-100kW magnetron, klystron or gyrotron in the 2.45 – 28 GHz range and/or you are interested in collaborations, please contact me at [email protected]
Full-Wave Modeling in the Electron Cyclotron Range, with Applications to a novel q-profile Diagnostic by
Oblique Reflectometry Imaging and Mode Conversions
F.A. Volpe1, M. Choi1, 2, O.M. Meneghini3
1 Columbia University, New York, NY
2 Present address: Imsol-X, San Diego, CA 3 Oak Ridge Associated Universities (ORAU), Oak Ridge, TN
Presented at the US-Japan Workshop on RF
September 25, 2013, Boston, MA (USA)
Motivation: pitch-angle measurements are of paramountimportance for numerous fusion applications
• Stability� q profile (BS and non-inductive currents)� Resistive Wall Modes (RWM)� Neoclassical Tearing Modes (NTM)� Error fields penetration� Edge Harmonic Oscillation (EHO) in Quiescent H-modes (QH)
• Transport� Internal transport barriers� H-mode transition� Magnetic field fluctuations for EM turbulence and understanding of
anomalous electron energy transport• Pedestal and pasma boundary
� Resonant Magnetic Perturbations (RMP)� Edge current density for peeling-balooning stability
• Advanced and hybrid scenarios� Distruption prediction� ELM suppression by RMP
Mostly needed at the edge, with high temporal resolution, 1D/2D/3D
Physical principle: idea of anti-radar magnetic diagnostic
1 O-mode beam of millimeter waves(33-75GHz) is obliquely injected in themagnetized plasma
2 Angular dependent mode conversion atthe O-mode cutoff
� partly reflected as O-mode� partly transmitted to X-mode
3 Angular-dependent mode conversionaffects reflected beam pattern, that willexhibit a hole when plotted as a function ofthe horizontal and vertical view angles
4 Reflected beam pattern provides info onthe magnetic pitch angle at the cutoff, inthe pedestal region
Benefits of the anti-radar technique
• Internal local magnetic measurement• Temporally and spatially resolved (reflectometer-like)• Measure magnetic fluctuations and 2D/3D magnetic structures• Frequency-resolved measurements ! radially resolved
measurements of the pitch angle• Same applicability of reflectometry (broader applicability that
EBE, which is limited to overdense EBW emitter plasmas)• Active diagnostic:
� Stronger signals with strong source� Noise subtraction by modulation� Control over injected frequency, for probing different radii
• Only depends on XO conversion (no BXO), less complicationsand fewer degradation mechanisms
Fundamental equations
O-mode to X-mode transmission efficiency at O-mode cutoff:
C = exp
(�⇡k0L
rY
2
⇥2(1 + Y )(Nz,opt �Nz)
2+N2
y
⇤)
O/X-mode dispersion relation for oblique propagation
n2? = 1� X
1� (Y sin ✓)2
2(1�X) ±h(Y sin ✓)4
4(1�X)2 + (Y cos ✓)2i1/2 � n2
z
wherek0 is the vacuum wavelengthL is the local density scalelengthY = ⌦e/!Nz,opt =
pY/(Y + 1)
H. P. Laqua, Phys. Rev. Lett 78 (1997)
Fundamental equations
Elliptical polarization required for pure pure O-mode oblique injection:
E�p
E✓p=
2
4 2i sin ⌧p
Y cos
2 ⌧p +q(Y cos
2 ⌧p)2 + 4 sin
2 ⌧p
3
5
PLASMA
J. L. Doane, Manual of Polarizer Miter Bend Fabricated by General Atomics
EBE imaging
• EBW emission for ! > !UH
• OXB conversion requires thepasma to be overdense! ⇠ n⌦e < !pe(⇢ = 0)
• Signal amplitude depends ontemperature
• complicated EBW trajectories• degradation mechanisms:
� collisional losses� at UHR back-conversion to
fast X-mode� conversion effeciency
degraged at O-mode cutoffdue to density fluctuations
Full wave modeling of anti-radar diagnostic with COMSOL
To demonstrate this as well as to assess the diagnostic capabilitiesand limitations, we modeled the wave scattering andmode-conversion processes by means of the finite-element COMSOLMultiphysics code in two dimensions (2D)
Initial sensitivity studies for mock-up DIII-D plasmas• injection angle• frequency
Simulations confirmed the presence of a minimum in reflectivity of anexternally injected O-mode beam, and confirmed that this minimumdepends on the magnetic field at the cutoff.
Simplified slab model to mimic DIII-D plasma parameters
• Slab cold magnetized plasma• Radially varying ne, Bz
• Oblique O-mode injection invacuum
PLASMA
0
10
20
30
40
50
60
70
80
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Freq
uenc
y [GH
z]
X [m]X [m]
Dens
ity [m
-3 ]Ma
gneti
c fiel
d [T]
0 0.5e+19 1.0e+19 1.5e+19 2.0e+19 2.5e+19 3.0e+19 3.5e+19
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
10 GHz oblique injection with ✓ = 70o and 30o
20 GHz oblique injection with ✓ = 70o and 50o
10 GHz, ✓ = 70
o
plasmaedge
20 GHz, ✓ = 70
o
plasmaedge
10 GHz, ✓ = 30
o
plasmaedge
20 GHz, ✓ = 50
o
plasmaedge
10 GHz oblique injection with ✓ = 70o and 30o
10 GHz, ✓ = 70
o
Ex /7⇥ 105 [V/m]
Ey /3⇥ 105 [V/m]
Ez /1⇥ 106 [V/m]
10 GHz, ✓ = 30
o
Ex /1.00⇥ 106 [V/m]
Ey /0.77⇥ 106 [V/m]
Ez /0.81⇥ 106 [V/m]
20 GHz oblique injection with ✓ = 70o and 50o
20 GHz, ✓ = 70
o
Ex /1⇥ 106 [V/m]
Ey /4⇥ 105 [V/m]
Ez /1⇥ 106 [V/m]
20 GHz, ✓ = 50
o
Ex /1⇥ 106 [V/m]
Ey /7⇥ 105 [V/m]
Ez /1⇥ 106 [V/m]
Total electric field at plasma edge
10 GHz
0
2e+11
4e+11
6e+11
8e+11
1e+12
1.2e+12
1.4e+12
0 0.2 0.4 0.6 0.8 1
Injected wave Re!ected wave
20 GHz
0
2e+11
4e+11
6e+11
8e+11
1e+12
1.2e+12
0 0.2 0.4 0.6 0.8 1
Injected wave
Re!ected wave
Conclusions and future work
This study gives confidence in the feasibility of the diagnostic andprovides a basis to interpret future experimental data.
Presence of L-mode cutoff complicates original intuitive picture, andunderlines importance of fullwave modeling
Future work• Increase operating frequency in the 33 to 75 GHz band• Inclusion of ne and B fluctuation• Inclusion of toroidal ripple effects• Extensions to full 3D model
