Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID D.L. Rudakov, J. A. Boedo, R. D. Lehmer*, R. A. Moyer, G. Gunner - University of California, San Diego J. G. Watkins - Sandia National Laboratories * Present address: Logicon Information Systems and Services, Moffett Field, CA Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 1
Abstract A method for the measurement of electron temperature with high spatial and temporal resolution was recently implemented on a fast reciprocating probe on the DIII D tokamak. The technique, previously used on TEXTOR, is based on detection of harmonics generated in the current spectrum of a single Langmuir probe driven by highfrequency sinusoidal voltage. The method was implemented on DIII-D with a drive frequency of 4 khz and with improvements such as fully digital processing and active voltage feedback, thus allowing temperature measurements with a bandwidth of up to 2 khz. Probe voltage and current were recorded at the sampling rate of 5 MHz and the amplitudes of the first (4kHz) and the second (8 khz) current harmonics were extracted by digital filtering The harmonics were also detected in parallel by analog circuits for comparison and feedback. Digital processing does not introduce any phase delays (as analog detection does), making the technique suitable for correlation measurements. Initial results from DIII D show good agreement with swept double probe and Thomson scattering data. The technique was shown to be capable of measuring all the terms contributing to the turbulent (conductive) heat flux. Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 2
Motivation for Fast Edge T e Measurements in DIII-D Fast measurements of the edge electron temperature are needed to: Measure the turbulent heat flux in the boundary of DIII-D in L and H mode Answer the questions: is the H-mode transport barrier primarily a particle convection barrier, or heat conduction barrier? is edge heat transport dominated by electrostatic turbulence as particle transport is? Evaluate errors in turbulent particle flux measurements due to neglecting T e fluctuations Obtain time-resolved RMS amplitudes, cross-phases, particle and heat fluxes, to compare with predictions of analytic theory and numerical simulations Study transient phenomena such as ELMs, dithering L-H transitions, etc. Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 3
~ T e Measurements Are Needed to Calculate Turbulent Particle and Heat Fluxes 1 ~~ Particle Flux: Gr ES = neθ Bϕ ~θ = ~ θ usually estimated as E ~θ θ ϕ ~ f ~ However, ϕ ~ p = ϕ ~ f + α kt e e where α ~ 3 possible large errors! E ϕ p T ~ e measurement desirable Heat Flux: n Q Q Q kt G e r ES 3 3 ~ ~ = conv + cond = e r + kteeθ 2 2 Bϕ T ~ e measurement necessary Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 4
~ Probe Techniques Suitable for T e Measurements Fast-swept single or double probes: Require high sweep voltage (to reach ion saturation) High power amplifier required; arcing problems likely High sampling speed requirements (to perform fit to I-V characteristic) Triple probes: Arguably, do not work well in strongly magnetized plasmas (where the ion Larmor radius is smaller than the pin separation) Spatial resolution is compromised for wavelengths smaller than the pin separation (can be corrected by special pin arrangements) Cable capacitance in the vacuum drive of the DIII-D reciprocating probe is too high to use this method at high frequencies (> 1 khz) Harmonic technique - chosen for DIII-D: eu >> kt e Relatively low sweep voltage requirements.4kte eu kt e Only one pin required high spatial resolution Relatively low sampling rate requirements: fsampl 5 f sweep Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 5
Diagnostic Basics: Current to a DC-Floating Probe Driven by High-Frequency Sinusoidal Voltage -I pr -I si <I pr > ωt V V V f U cos(ωt) ~ I pr ωt V pr Non-linearity of the probe s I-V characteristic causes generation of harmonics in the current spectrum To satisfy <I pr > = operating DC potential of the probe is shifted from the floating potential: V = V f V where kt eu V = e ln I e kte U - drive voltage amplitude (Boedo et al, Rev. Sci. Instrum. 7 (1999), 2997) Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 6
Diagnostic Basics: Harmonic Expansion of the Probe Current Probe current for V pr < V p (plasma potential) is given by: e( Vpr V p) e( V I pr = I + I = se exp I + I se exp si si k T e e( V V p) eu cos( t) + I si se exp exp ω k T e k T e = I Using exp( z cos( θ )) = I( z) + 2 Ik ( z)cos( kθ ) one can get: k= 1 2I I si eu I eu cos( ) pr = m mωt I cos( m t) eu I m 1 kte m 1 m = ω ω kte = = kt e eu eu eu where I m = I ω 2 si Im I - amplitude of m th harmonic kte kte kte Ik ( z) - Bessel functions of integer order k + U cos( ωt) V k T e p) = Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 7
Diagnostic Basics: Series approximation for eu /kt e < 1 Bessel functions can be expressed by a series: For z << 1 only the first term can be used: Hence, for eu /kt e << 1: eu eu I 1 kte 2kT e eu I 2 kt e 1 8 eu kt e 2 I k ( z) Ik ( z) = eu I 3 kt e z + n= 2 2 n k k z 2 k k! 1 48 eu kt e 2n+ k ( n + k)! n! 3 eu I1 eu I kt ω e = 4 I2 4 I2ω Thus T e can be determined from the ratio of the amplitudes of 1 st and 2 nd harmonics The error of this approximation for eu /kt e = 1 is only about 5% (Boedo et al, Rev. Sci. Instrum. 7 (1999), 2997) Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 8
Diagnostic Layout - Original (TEXTOR) Probe Voltage divider Amp Peak detector V f drive = 4 khz 25 W RF amp Pearson coil Amp 4 khz Bandpass filter Amp Peak detector I w 8 khz Bandpass filter Amp Peak detector I 2w Optional center tap tranformer to compensate capacitive leakage current through transmission line Dummy transmission line Current harmonics detected by band pass filters and fast (1 khz) peak detectors Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 9
Capacitive Leakage Current I ω (A).3 -.3.1 I ω (A) 2I c I c 2.75 2.76 t (ms) 2.77 1 st current harmonic I ω after filtering detected amplitude of I ω (averaged over.2 ms) 2.78 The offset I c in the amplitude of the 1 st current harmonic I ω is caused by capacitive leakage to the ground in the transmission line to the probe For constant drive voltage amplitude I c can be substracted from the detected amplitude of I ω Simple substraction will not work with voltage feedback in place Leakage current can be compensated using a center tap transformer and a matched dummy transmission line Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 1
Diagnostic Upgrade: Drive Voltage Feedback For the linear approximation to work and to avoid approaching electron saturation, the drive voltage amplitude U should be kept below T e For the signal to noise ratio to be high enough the amplitude of the second harmonic should be large enough I 2ω.1 I ω Therefore U should be kept in the following range: kt.4 e e U kt e e As the probe plunges towards the separatrix, T e changes from below 1 ev to above 1 ev, therefore, drive voltage feedback is necessary Practically voltage feedback can be implemented by using an analog divider to determine the ratio of current harmonics (or U / T e ) and providing feedback to the function generator to keep this ratio within required limits Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 11
Diagnostic Layout - Upgraded (D-IIID) Probe f drive = 4 khz 25 W RF amp C1 C2 C3 R1 Pearson coil R2 Amp Amp V_fast Amplitude detector 4 khz Bandpass filter V Amp I w Amplitude detector Adder Upgrades: V_min Tunable LPF Analog multiplier Dummy transmission line Comparator I_min Amp I_fast 8 khz Bandpass filter I w /I 2w Fully digital processing Drive voltage feedback Slow (1 khz) T e output for long pulse capability Ref Ref Analog multiplier Amp Analog divider I 2w Comparator Amplitude detector T e _slow Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 12
Digital Filtering Digital filtering is performed in IDL using standard IDL functions DIGITAL_FILTER and CONVOL Filters typically used are Finite Impulse Response (FIR) Kaiser filters of the order N = 4 1 with ripple amplitude A < -5-1 db and pass band half-width df = 1 2 khz db -2-4 -6-8 -1 4 1 5 8 1 5 1.2 1 f (Hz) 5 Frequency responses of FIR Kaiser filters used for first and second current harmonics Filter parameters: N = 1 A < -1 db df = 1 khz Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 13
Digital Filtering Does Not Introduce Phase Delay Raw current signal and harmonic signals obtained by digital filtering.1 (V) -.2.15 (V) -.15.15 (V) -.15.1 ms Raw current I_fast First harmonic I ω (4 khz) Second harmonic I 2ω (8 khz) Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 14
Digital Harmonic Detection Is Superior to Analog Amplitude of the 1 st current harmonic obtained by analog and digital methods.25 analog analog I ω (A).25 I ω (A) digital digital ~ 1 µs.25 ms Analog circuitry introduces time delay of about 1 µs making it not suitable for correlation measurements at high frequencies 1 ms (probe plunge) Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 15
Results: Raw Signals and Feedback Operation Shot # 1224 236 R (cm) 224 6 U (V) -6.8 I (A) Probe position (a) R = 226.4 cm sep (b) Probe voltage (c) Probe current (d) Calculated temperature -.6 12 Te (ev) 1.44 1.46 t 1.48 t (s) 1.5 1.52 At t = t feedback turns on and keeps the ratio Te/U within preset limits Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 16
Results: Comparison with Swept Double Probe and Thomson Scattering Te (ev) 12 1 8 6 4 2 Shot # 1224 Thomson scattering Swept double probe Harmonic technique Harmonic technique and Thomson scattering are in good agreement throughout the range Double probe gives lower temperatures inside the separatrix due to the drive voltage being not high enough to reach ion saturation.95 1. 1.5 1.1 1.15 ψ N Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 17
Results: Edge Electron Temperature Fluctuations 4 4 ms Shot# 131 T e (ev) T e (ev) 4 15 4 ms a.u. T e (ev).6 ms Fluctuating Temperature on Different Time Scales 1 3 1 4 1 5 f (Hz) Power Spectrum of the Temperature Fluctuations Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 18
Results: Terms Contributing to Turbulent Heat Flux Q cond ~ T e amplitude = q( ω)dω, a.u 3 n rms rms q ( ω) = e Te ( ω) E ( ω) γ ( ω)cos( α ( ω)) 2 θ TE TE Bϕ rms T e (ω) 1 γ TE (ω) coherence ~ E θ amplitude a.u a.u E θ rms (ω) P TE (ω) 4-4 a.u α TE (ω) q(ω) crosspower crossphase heat flux spectral density f (Hz) 1 5 f (Hz) 1 5 Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 19
Q cond (W/cm 2 ) Results: Measured Heat Flux and Power Balance Conductive heat flux can be estimated in time domain as: Q 12 1 cond 8 6 4 2 = 3 2 n B e ϕ ~ ~ kt E e θ Shot # 1224 3 2 n B e ϕ 1. 1.1 1.2 ψ N ~ kt rms e ~ E rms θ γ TE cos( α TE In this shot during the probe plunge: Input power: P in = P NBI + P Ohmic 2 MW Radiated power: P rad.6 MW Conducted power: (assuming γ TE cos(α TE ) =.5) P cond = Q cond S LCFS 1.5 MW Same order of magnitude: P cond ~ P in - P rad ) Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 2
Summary Harmonic technique has been implemented on D-IIID with upgrades including fully digital processing and drive voltage feedback Digital harmonic detection does not introduce phase shifts making the system suitable for correlation measurements First T e results from DIII-D are in agreement with swept double probe and Thomson scattering data First measurements of the turbulent heat flux in DIII-D have been performed Measured heat fluxes are consistent with power balance Fast Electron Temperature Diagnostic Based on Langmuir Probe Current Harmonic Detection on D-IIID - D.L. Rudakov et al - 21