Differential Interferometry for Measurement of Density Fluctuations and Fluctuation Induced Transport

Differential Interferometry for Measurement of Density Fluctuations and Fluctuation Induced Transport Liang Lin University of California, Los Angeles, California, USA in collaboration with W. X. Ding, D. L. Brower, W. F. Bergerson, T. F. Yates University of California, Los Angeles, California, USA A. F. Almagri, K. J. Caspary, B. E. Chapman, J. S. Sarff, T. Tharp University of Wisconsin Madison, Madison, Wisconsin, USA 18 th Topical Conference High Temperature Plasma Diagnostics May 16 20, 2010 Wildwood, New Jersey

n E n( V B ) 0 r Total Flux Pinch Electrostatic Motivation Particle transport plays an important role in the fusion plasmas E ne nb V b n V n 0 r // r 0 0 0 B0 B0 B0 B0 ITG TEM ETG Electromagnetic -Energetic particle driven modes Resonant magnetic perturbation (RMP) Tearing instabilities Gradient of density fluctuation is necessary to study the dynamics of density evolution. n e nv 0 0 nv t How to measure density fluctuations, gradient of density fluctuations, and fluctuation induced particle flux Elimination of fringe sips is important for interferometry (on ITER)

Outline Differential Interferometry Principle Experimental Setup Calibration techniques Plasma Wedge Applications resolving density profile evolution in a pellet fueled plasma measuring particle flux and three wave coupling in a stochastic magnetic field

Differential Interferometry 1. Standard interferometer measures phase shift induced by plasma, x n x z dz int e, 2 2 a x int e 2 2 a x e x r n r dz Abel Inv. n () r e 1 a int ( x) dx r r e x x r 2 2 2. Differential interferometer directly measures the phase difference between two adjacent chords, x int x thereby providing a more direct determination of local density profile. int

Differential interferometry employs two parallel laser beams with small spatial offset (x) and frequency difference () Linearly Polarized Linearly Polarized plasma x ~ 1mm ndz int e Ref. Mixer int z x int int int x 2 Signal Mixer x 2

Third FIR cavity permits a simultaneous operation of a standard interferometer Linearly Polarized Linearly Polarized plasma ndz int e x ~ 1mm x int ~ x x int 1 int 2 2 Ref. Mixer z Local Oscillator Signal Mixer x

Standard differential interferometry configuration permits simultaneous measurements of density profile and its gradient ndz 2 3 3 Differential Interferometry : int e 2 2 int x x 1 Three frequency peas correspond to mixing between three FIR lasers. x int ~ 3 x int 1 x 3 int x2 int x1 int x2 x int ~ int Standard Interferometry: 2

Three wave FIR laser system allows for multiple interferometry configurations Standard interferometry: x n dz n n int e e, e Differential interferometry: / int x, n Faraday Rotation: n e e x n B dz B b pol, e z r 11 chords, x ~ 8 cm, phase ~ 0.05 o, time response ~ 1s See Poster D31, W. X. Ding

Accurate calibration of xis essential before any application of differential interferometry Linearly Polarized ~ 1-3 mm Waveguide Metallic wire meshes Mirrors Linearly Polarized plasma x due to complicated optical system x Ref. Mixer z LO Beam 3 Signal Mixer

Not feasible to accurately distinguish a 1 mm spatial offset between two probe beams by direct profile measurement Beam spatial offset (x~1 mm) is small compared to the FIR beam diameter (w beam ~40 mm) 40 mm Beam profile measurements are time consuming and cannot be made in vacuum vessel requires development of independent calibration technique 40 mm

Spatial offset Calibration Plasma Wedge

Calibration accomplished by matching standard and differential interferometry measurements xis determined by minimizing: diff. / 2 i x i x i stand. i 2 x = 1.48 mm i diff. : where Differential interferometry data; x stand. i : Derivative of standard interferometry data; i : i diff. Uncertainty of ; i : Channel number.

Plasma calibration method limitations requires simultaneous operation of standard and differential interferometry accuracy is limited by the performance of the standard interferometry Plasma independent calibration method is desired

Principle of Plasma Independent Calibration Method Passing two probe beams with spatial offset through a dielectric wedge introduces a phase difference 2 n wedge nair x FIR tan is nown ( 0.5 o ), diffraction effect is insignificant. is measured by differential interferometry. x 2 / n n tan FIR wedge air

Wedge is placed on a rotating stage to mae easily detectable 0 o 90 o is observed to sinusoidally vary as the wedge rotates, i.e. sin 1 0 x 2 / n n tan 1 FIR wedge air

Wedge calibration has a few advantages Two calibration methods give a similar offset, Plasma Wedge x 1.48 0.30 mm x 1.38 0.08 mm The wedge calibration has a few advantages: plasma independent does not require the third FIR laser for the simultaneous operation of standard interferometry high resolution (uncertainty below 0.08 mm) wedge calibration can be used to align two beams co linear for Faraday rotation measurement

Application I Density profile evolution in a pellet fueled plasma Differential interferometry is immune to fringe sip errors

Differential interferometry is immune to fringe counting errors Standard Interferometry Differential Interferometry Mixer Signal Signal is momentarily lost due to refractive effect; fringe counting error occurs when the signal is recovered.

Application of standard interferometry is limited by fringe counting errors in harsh plasma environments Standard Interferometry difficult to numerically remove all fringe sips. Manual correction is time consuming and biased. Accuracy can be further improved by adding differential data constraint Differential Interferometry Sign change indicates hollow profile

Local density profile can be obtained from the differential interferometer (by itself) hollow profile confirmed by direct measurement of gradient sign change Extraction of density profile from the differential interferometry data is much simpler and does not involve in complicated and potentially biased phase error correction process

Differential interferometry is immune to fringe sip errors and is particularly useful in harsh plasma environments This advantage maes differential interferometry a diagnostic option worth considering for ITER

Application II nonlinear interactions via three wave Coupling Differential interferometry has high spatial and phase resolution required to determine the gradient of density fluctuations.

Multiple magnetic tearing modes are present in MST Magnetic field lines are strongly sheared. Tearing modes resonant where B0 m n BP BT r R q r m n Tearing mode growth results in magnetic reconnection and leads to abrupt sawtooth crash. 0 q rb RB T P reversal surface

Density relaxation occurs during sawtooth crash Multiple Tearing Modes Stochastic Magnetic Field Particle Transport Density relaxation Crash time < 200 µsec. Collision time τ e,i ~10 msec. >2000 events

Magnetic fluctuation induced particle flux can account for fast density relaxation at sawtooth crash Interferometry: (Total Particle Flux) n e t S total re, 1 At ne r, t dv r/ a~0.3 Interferometry + Polarimetry: (Magnetic fluctuation induced flux) V mag re, //, e nb J r nb r B ne B 0 0 re total mag re,, r/ a~0.3

Evaluation of three wave coupling is necessary to investigate the cause of density fluctuations Power Balance of Density Fluctuations Power Term Linear term Nonlinear term 1 2 n 2 n n 0 nv r, nv r, t r r 1 3 1 1 1 2 2, 3 In steady state, 1 nv nv n n0, 1 1 1 1 2 3 2 3 Many quantities are required to determine the time evolution of density fluctuations.

Three wave FIR system allows for the evaluation of all terms in the power balance of density fluctuations Power Term Linear term Nonlinear term 1 2 n 2 n n 0 nv r, nv r, t r r 1 3 1 1 1 2 2, 3 Interferometer Polarimeter + Edge magnetic measurements n n and r b r, V r, Ve, B 0 0 Linear term nv r, 1 1 n r 0

Gradient of density fluctuations is critical to three wave coupling Power Term 1 2 n Linear term Nonlinear term 2 n n 0 nv r, nv r, t r r 1 3 1 1 1 2 2, 3 Interferometer Polarimeter + Edge magnetic measurements n n and r b r, V r, Ve, B 0 0 Nonlinear term, 2 3 nv r, 1 2 n r 3 Differential interferometer n r and n 0 r

Differential interferometry measures gradient of density fluctuations Standard Interferometry Differential Interferometry r ~ 0.43 m r/ a~0.8 Fluctuation radial scale length L n L n n n / r ~ 2 cm a 52 cm

High spatial resolution of differential interferometry permits measurement of small scale fluctuations r/ a~0.8 Fluctuation radial scale length L n n n / r Chord separation of standard interferometry (~ 8 cm) is limited by access (port) constraints Chord separation of differential interferometry ( < 0.3 mm) is not limited by spatial constraints since two probe beams with spatial offset share the same optical components and detection system

Differential interferometry provides local measurement of density gradient and its fluctuations For density gradient and its fluctuation ( x) n ( r) dz x e ( x) ne () r r dz x r x x x ne () r cos dz r Z (cm) 40 20 0-20 x=2 cm x=21 cm Geometrical factor leads to weighted line integral. Z -40 cos x r 0.2 z 0.4 0.6 cos( r x 0.8 1.0

Both linear advection and nonlinear three wave interaction are important to particle transport. m1, n1 (1, 10) Linear term n nv 1 r, 1 r 0 r/ a~0.8 Nonlinear term n nv 1 r, 2 r, 2 3 3 Power Term 1 2 n 1 t 2 Both the amplitude and sign of nonlinear term can be determined

Summary Differential interferometry allows for measurements of the electron density gradient, its fluctuations, as well as the equilibrium density. Accurate calibration of the probe beam spatial offset is critical for general application and is accomplished by use of a rotating dielectric wedge. Differential interferometry is immune to fringe sip errors and is particularly useful in harsh plasma environments. Differential interferometry has high spatial resolution and permits measurement of small scale fluctuations. Calibrated differential interferometer has been successfully used to (1) resolve density profile evolution during pellet injection, and (2) measure three wave coupling in a stochastic magnetic field