Detection of Lower Hybrid Waves on Alcator C-Mod with Phase Contrast Imaging Using Electro-Optic Modulators K. Arai, M. Porkolab, N. Tsujii, P. Koert, R. Parker, P. Woskov, S. Wukitch MIT Plasma Science and Fusion Center
1. Electro-optic modulator to detect LH waves in PCI system is proposed
Alcator C-Mod uses 1-3 MW of lower hybrid (LH) power for current drive at 4.6 GHz. LH wave dispersion Combined with Poisson s Equation, the electron density fluctuation is estimated
PCI is an interferometry technique The unscattered beam π/2 phase shifted 4
Density fluctuation shifts the laser phase : Classical electron radius Assume sinusoidal fluctuation 5
PCI signal is linear in Unscattered beam phase shifted by π/2 6
PCI setup in Alcator C-Mod R = 60-79 cm OPM M Phase plate M plasma M Detector extra phase π/2 M LASER CO₂ 80W CW Inside the cell OPM M M: mirror OPM: off-axis parabolic mirror Modulator M
Detector HgCdTe photoconductive 32 channel array Detector frequency bandwidth ~ 10 MHz -> Need laser beam amplitude modulator for optical heterodyne detection of lower hybrid wave signals (~ 4.6 GHz)
Electro-optic modulator is suitable for GHz amplitude modulation An external E-field changes electro-optic crystal s refractive index. ( 2 nd order nonlinear effect ) Electro-optic effect : electro-optic coefficient, determined by crystal s group structure
A laser beam will see this effect as its difference phase shift between the two polarizations. -> phase shift is proportional to applied voltage. Sinusoidal applied voltage produces amplitude modulation. crystal should be transparent at 10.6 μm -> CdTe electric field aiming for 1-10 kv/cm -> Cavity resonator
2. Electro-optic amplitude modulation with Cadmium Telluride
Cadmium Telluride has zincblende structure 4-fold Group properties - Space group: 43m - Electro optic coefficient: 3-fold Three directions of symmetry m/v
Apply E-field into (110) plane (c) (1 1 0) z Γ = 0 y 45⁰ Γ = 0 y z 45⁰ 45⁰ Γmax x Γ = 0 x E
Index ellipsoid is changed by the applied E-field Coordinate transformation new refractive index Phase shift
Sandwiching the crystal with wave plate and polarizer produces amplitude modulation π/4 plate polarizer Transmitted laser field amplitude where
3. Design parameters are determined with maximum modulation efficiency
Electro-optic modulator is designed with CST Laser path Port Coaxial cable in. radius 1.3 mm out. radius 3.0 mm impedance 50 Ώ CdTe crystal (3*3*35 mm)
CdTe is embedded in a cylindrical cavity resonator with mode Electric field as a function of x Consider transient time effect where
Minimum input power is obtained by adjusting the crystal length
Simulation shows a resonance (Q=1000) S-parameter magnitude in db Frequency [GHz]
Electric field distribution(2d plot) Calculated with 1 W input power. Dielectric constant of CdTe crystal is 6.76-7.13. E-field in the crystal is about 7 times smaller.
V/m Magnitude of field along the crystal Length [mm]
Simulation shows input power: 1W calculated electric field: 9000 V/m Experiment requires electric field for 60 % modulation: V/m -> required input power is I = 40 kw! This may be too high to avoid breakdowns
Three suggestions to reduce input power 1. Reduce modulation efficiency down to 10 % -> I = 400 W 2. Use rectangular cavity resonator -> I = 8 kw 3. Find resonance with higher Q factor (ex. change material to silver)
4. Conclusions / future work
EOM for detection of LH waves in Alcator C-Mod is proposed. CdTe crystal has good properties for GHz amplitude modulation of CO₂ (simple electro-optic coefficient, transparency at 10.6 μm ) Design parameters are determined requiring maximum modulation efficiency and minimum input power.
Future work Further reduce the required input power. Need to simulate heat flow of the cavity resonator and energy dissipation on the crystal. Further detailed design and fabrication are the next step.