Overview of plasma diagnostics (high energy density plasmas) S.V. Lebedev Imperial College London General comments HEDP systems emit: • Visible, XUV, x-ray photons • Charged particles • Neutrons Can be probed by similar particles Small objects – high spatial and temporal resolution (10m, 1ns) Principles of plasma diagnostics are mostly common for all types of plasmas 2 [email protected] May 2019 Outline Electrical measurements: magnetic field and current Laser probing: interferometry, density gradients Emission: spectral lines, continuum Thomson scattering X-ray imaging Proton probing 3 [email protected] May 2019 Magnetic field Magnetic coil E dl B ds V NAB C S RC after integrator: B(t) V (t) NA int Example of magnetic probe designed to measure magnetic field distribution inside the plasma More often a set of coils outside Always check absence of capacitive coupling! (rotation of coil by 1800 should give identical signal but of opposite polarity) 4 [email protected] May 2019 Magnetic field Magnetic coil E dl B ds V NAB C S RC after integrator: B(t) V (t) NA int Example of magnetic probe designed to measure magnetic field distribution inside the plasma More often a set of coils outside Always check absence of capacitive coupling! (rotation of coil by 1800 should give identical signal but of opposite polarity) Recent design: dif. ampl. of oppositely wounded coils (Bx, By, Bz) (100MHz) [Everson et.al, RSI 80, 113505 (2009)] 5 [email protected] May 2019 Magnetic field Magnetic coil E dl B ds V NAB C S RC after integrator: B(t) Vint (t) NA B-probe Magnetic probes in HEDP: • Usually positioned at some distance from the object – require extrapolation of the measured signal to the object (sometimes by many orders of magnitude) • Can be strongly affected by a “noise” from energetic particles generated in the system (can be tested using two oppositely-wound probes) Measured: 5 mT at 3cm from the coil Extrapolated: 800 T in the coil 800/5x10-3 = 1.6x105 Santos et al, NJP, 17, 6083051 (2015) 6 [email protected] May 2019 Rogowski coil Gives total current through the loop, independent on current distribution. (if the signal is not “too fast”, i.e. > propagation time along the coil) I n dAB dl B dl 0 I lA l nA0 I V nA0 I • n is number of turns per unit length, A is area of the coil cross-section • Induced voltage is proportional to dI/dt (V can be integrated before recording) • “Return wire” to exclude contribution from magnetic flux through the coil • needs electrostatic shielding 7 [email protected] May 2019 Probing by E/M waves Plasma object Laser beam Detector Change of phase velocity Refraction of the beam (deflection, broadening) Rotation of polarisation plane (Faraday effect) 8 [email protected] May 2019 Refractive index measurements Propagation of electro-magnetic waves c phase shift (interferometry) Vph k refraction of the beam (schlieren and sadowgraphy) rotation of polarisation plane (Faraday effect) Refractive index of plasma without magnetic field: 2 21 2 2 2 2 p ne 3 1.1210 p k c (1 2 ) (1 ) ncr [ cm ] 2 ncr [ m] Probing beam cannot propagate Cut-off densities: if the plasma density is above 337m (HCN laser) n = 1016cm-3 the critical density cr 19 -3 10.6m (CO2 laser) ncr = 10 cm 21 -3 1.06m (Nd, ) ncr = 10 cm . 21 -3 0.532m (Nd 2) ncr = 4 10 cm 9 [email protected] May 2019 Interferometry Mach-Zehnder and Michelson configurations Signal on the detector: 2 2 2 2Er E p Et (Er E p )[1 2 2 cos()] (Er E p ) 2.0 intensity split: 50% / 50% 20% / 80% Equal intensities 1.5 5% / 95% of the probing and reference 1.0 beams give the best visibility of Phase shift (typically ne<<ncr): 0.5 the fringes (k pdl krdl) 0.0 0510 n Line density corresponding to one fringe: [ 1 e 1]dl n dl e 337m (HCN laser) n L = 6.6.1014cm-2 c ncr 2cncr e 10.6m (CO laser) n L = 2.1.1016cm-2 Number of fringes: 2 e . 17 -2 1.06m (Nd, ) neL = 2.1 10 cm 18 F 4.4610 [m] 2 nedl . 17 -2 2 [cm ] 0.532m (Nd 2) neL = 4.2 10 cm For “cw” plasmas need to exclude vibrations (two wavelength interferometry) 10 [email protected] May 2019 Interferometry Refractive index for neutral gases fi,k is an oscillator strength for i to k transition 2 fi,k ni 1 (2 e / m) ik is the frequency of transition a 2 2 i,k (ik ) ni is the density of atoms in state i For optical frequencies far from spectral lines ( is polarizibility): Phase shift: 2 (1)dl a 1 2 na Number of fringes due to electrons and atoms: Atom 2 2 He 1.3.10-24 cm3 F 4.461014 n dl n dl [cm] e a . -24 3 2 H2 5 10 cm •different sign of phase shift for electrons and atoms Air 1.1.10-23 cm3 [e.g. for H =0 at n /n =2.2% (0.56% for He) @ 6943Å] Ar 1.10-23 cm3 2 e a •different dependence on Al 4.4.10-23 cm3 11 [email protected] May 2019 Interferometry Mach-Zehnder and Michelson configurations Signal on the detector: 2 2 2 2Er E p Et (Er E p )[1 2 2 cos()] (Er E p ) 2.0 intensity split: 50% / 50% 20% / 80% Equal intensities 5% / 95% 1.5 of the probing 1.0 and reference beams give the 0.5 best visibility of Phase shift (typically ne<<ncr): the fringes 0.0 (k dl k dl) 0510 p r n Line density corresponding to one fringe: [ 1 e 1]dl n dl e 337m (HCN laser) n L = 6.6.1014cm-2 c ncr 2cncr e 10.6m (CO laser) n L = 2.1.1016cm-2 Number of fringes: 2 e . 17 -2 1.06m (Nd, ) neL = 2.1 10 cm 18 F 4.4610 [m] 2 nedl . 17 -2 2 [cm ] 0.532m (Nd 2) neL = 4.2 10 cm For “cw” plasmas need to exclude vibrations (two wavelength interferometry) 12 [email protected] May 2019 Interferometric imaging Wide probing and reference beams to produce 2-D image of plasma Misalignment between the beams () d reference fringes ( d = / [2.sin(/2)] ) in the regions without plasma Fringe shift due to plasma map of neL Practical lower limit ~1/10 – 1/30 of fringe Shear interferometer (best for small plasma objects) Magnified beam is used as a reference Numbers show fringe-shift in a particular position M. Tatarakis et al, PoP, 5, 682 (1998) 13 [email protected] May 2019 Simple Example: Interferogram of 8 Wire Tungsten Array Initial wire position Ablation Stream Axis Analysis method: [Swadling et al. ‐ PoP 20, 022705 (2013)] Trace experimental and background fringes: Number fringes, interpolate and subtract Number Interpolate Subtract Phase Fringes Phase Fields More Complex example – 32 wire Al array Results published ‐ Swadling et al. ‐ Physics of Plasmas 20, 022705 (2013). More Complex example – 32 wire Al array Results published ‐ Swadling et al. ‐ Physics of Plasmas 20, 022705 (2013). Schlieren and shadow imaging Transverse density gradients deflect the probing beam Light source schlieren shadow y shape x dl Knife plasma edge Image plane Deflection angle: Knife to measure 1-D gradients Intensity distribution d 1 d pin-hole for “bright-field” schlieren dl n dl I d 2 d 2 e L dl dy 2ncr dy 2 2 disk for “dark-field” schlieren I dx dy Example: (If an imaging system between the object and the . -3 =2 10 rad, =532nm Bow-shock at detection plane is used, then . 19 -3 an obstacle L is the plasma length) nedl = 1.5 10 cm Jet boundary shock Supersonic plasma jet 19 [email protected] May 2019 Example: plasma jet – obstacle interaction Supersonic magnetized plasma jet interacts with an obstacle (experiments on MAGPIE facility at Imperial College): Obstacle 18 -3 (d=0.5mm) ne ~ 10 cm , Vjet ~ 100km/s, = 5.10-3rad, =532nm Bow-shock Schlieren image highlights the positions of sharp gradients: bow-shock and collimation shock at the jet boundary Plasma jet Interferogram allows measurements of the electron density in the regions where interference fringes are traceable Flow direction 20 [email protected] May 2019 Faraday rotation Linearly polarised wave is superposition of two circularly polarised. Difference in refractive indexes of the two waves leads to rotation of polarisation plane Rotation of polarisation plane: e n B dl e n e e B dl 1/ 2 2mec ncr (1 ne / ncr ) 2mec ncr 17 2 2.2610 n 3 B dl [rad ] [cm] e[cm ] [G] Example: 19 -3 5 0 ne=10 cm , B=10 G (10T), =532nm, L=1cm => =3.67 Magnetic field can be found if the density distribution is known Convenient to combine with interferometry M. Tatarakis et al, PoP, 5, 682 (1998) 21 [email protected] May 2019 Faraday rotation ( at ± β from extinction ) Detector Probe beam Faraday Polariser Self-emission sensitivity intensity rotation angle angle I x, y 2 2 SE I s I sin I S s x, y I S x, y sin x, y B B 2 1 I x, y I x,y I x,y tan x, y sin1 B S S I B x,y I B x,y 2 I S x, y 2 G.