(LASER) PLASMA DIAGNOSTICS Leonida A. Gizzi Intense Laser Irradiation Laboratory Istituto Nazionale di Ottica – CNR Pisa, Italy la.gizzi@ino.it

DENSITY: USE OPTICAL PROBING Dt Probe pulse ANALYZER Plasma Interaction of fs pulses with gas-jets; Short-pulse interferometry Phase shift and Fringe Visibility Depletion Time-resolved propagation with pump and probe approach

OPTICAL PROBING ANALYZER SHADOWGRAPHY: MAP OF TRANSPARENT PLASMA Dt Probe pulse ANALYZER Plasma SHADOWGRAPHY: MAP OF TRANSPARENT PLASMA KNIFE-EDGE (SCHLIEREN): MAP OF DENSITY GRADIENTS INTERFEROMETRY: MAP OF DENSITY POLARIMETRY (FARADAY ROTATION): MAP OF MAGNETIC FIELDS

EXAMPLE: OPTICAL PROBING OF CPA PROPAGATION IN GASES The position of the focus relative to the jet is usually a critical parameter probe beam gas jet main pulse Fine tuning nozzle 3mm x 300µm slit or 1mm diam cyl.

Interferogram taken after pulse propagation: T=+5 ps EVIDENCE OF ASE EFFECT Depending on the relative position of best focus and gas jet, early ionisation may take place due to Amplified Spontaneous Emission. ASE-induced precursor plasma 200 µm Second Harmonic emission from main CPA Main laser pulse GAS ionised by CPA Interferogram taken after pulse propagation: T=+5 ps Simultaneous detection of electron energy spectrum and plasma interferometry enables identification of the role of ASE

PLASMA INTERFEROMETRY Dt Probe pulse Plasma fringe pattern phase difference electron density The phase difference map is obtained from the fringe pattern with FFT analysis (M. Takeda, H. Ia, and S. Kobayashi, J. Opt. Soc. Am. 72, 156, (1988), L.A.Gizzi et al. Phys. Rev. E, 49, 5628 (1994)), or with an original numerical technique based on Wavelet Transform (P. Tomassini et al., Appl. Optics, 40, 6561 (2001)) The electron density map is obtained from the phase difference map with an original algorithm based on Abel inversion extended to moderate axial asymmetric distributions: P. Tomassini & A. Giulietti , Optics Comm. 199, 143 (2001)

OPTICAL DIAGNOSTICS: FEMTOSECOND INTERFEROMETRY All-optical way to retrieve the electron density map of the accelerating medium Exploit a laser beam to probe the plasma via its refractive index effect on the interference fringe pattern Use of ultrashort laser pulse enables femtosecond resolution measurements i.e. : Mach-Zehnder interferometer From the refractive index we can get to ne… • L.A. Gizzi et al., AIP Conf. Proc. Vol. 827, 3 Editors M. Lontano et al., Melville, N.Y. (2006). • L.A.Gizzi et al., PRE, 2009

THE NOMARSKI INTERFEROMETER It’s an in-line set-up Enables control of imaging parameters (resolution, f.o.v …) R.Benattar et al, Rev.Sci.Inst. 50(12),1583 (1979) O.Willi, in Laser-Plasma Interactions 4, Proceedings of the XXXV SUSSP, St. Andrews, 1988, edited by M.B. Hooper (SUSSP, Edinburgh, 1989). L.A.Gizzi et al. Phys. Rev. E 49, 5628 (1994); M.Borghesi et al., Phys. Rev. E 54 , 6769 (1996).

BASIC PRINCIPLES Comparing the phase difference between the two arms: The total phase shift in the plasma arm (WKBJ approx.) is: Comparing the phase difference between the two arms: The plasma refractive index is nc (0.4 m)  6.91021 cm-3 that can be inverted to obtain ne(x,y,z) (under suitable geometrical symmetry, i.e. cylindrical) Abel inversion P. Tomassini et al., Appl.Opt., 40(35):6561, (2001).

INTERFEROMETIC MAP FROM EXPLODING FOIL PLASMA TARGET LASER PLASMA LASER PROBE … FFT analysis M. Takeda, H. Ia, and S. Kobayashi, J. Opt. Soc. Am. 72, 156, (1988)

EXAMPLE FFT OF INTERFEROGRAM

RECONSTRUCTED ELECTRON DENSITY MAP

Geometry of beam propagation (He) T= +1.34 ps #141255 200 µm f/2.5

Geometry of beam propagation T= +2.33 ps #141260 200 µm f/2.5 Region of loss of fringe visibility

Geometry of beam propagation T= +4.67 ps #141267 200 µm f/2.5

Loss of fringe visibility Longitudinal Transverse

Fringe pattern: modelling - 1

Fringe pattern: modelling - 2

Fringe pattern: modelling - 3 Phase shift L.A.Gizzi et al. Phys. Rev. E, 49, 5628 (1994); Fringe visibility

Advanced: Optical probing of Laser Wakefield Wakefield structure: >Electron density modulations (≈1%); >Fast evolution(fs) >Small spatial scale (µm) Under Self-injection conditions: >High current electron bunch(es); >Azimuthal magnetic field generation; In general, INTENSITY, PHASE and POLARIZATION of a probe pulse will be affected.

Optical probing of Laser Wakefield INTENSITY MODULATIONS: In a Shadowgraphy or Schlieren (knife-edge) configuration, measurements will show (qualitatively) density modulations due to absorption or refraction effects; POLARIZATION ROTATION: Plane of polarization of linearly polarized light propagating in a magnetic field parallel to the k-vector will rotate (Faraday rotation). Polarimetric analysis of the beam will yield map of the B-field component along k.

Experimental Setup Courtesy of

Faraday-Rotation Transverse probing of B-fields in underdense plasma with linearly-polarized probe pulse: if  B-field induced difference of h for circularly- polarized probe components  rotation of probe polarization:  measure frot to get signature of B-fields! J. Stamper et al. Phys. Rev. Lett. (1975)

EXPERIMENTAL SET-UP

JETI-Results: Faraday-Rotation Two polarograms from two (almost) crossed polarizers: polarogram 1 560 µm 340 µm polarogram 2

JETI-Results: Faraday-Rotation Two polarograms from two (almost) crossed polarizers: polarogram 1 560 µm 340 µm polarogram 2 Deduce rotation angle frot from pixel-by-pixel division of polarogram intensities:

JETI-Results: Faraday-Rotation polarogram 1 560 µm 340 µm polarogram 2 simulated feature experimental Faraday feature Experimental evidence for B-fields from MeV electrons and bubble! MCK et al., Physical Review Letters 105, 115002 (2010)

LWS-20 Results: Faraday-Rotation Two polarograms from two (almost) crossed polarizers: polarogram 1 polarogram 2 Electron bunch length: z = 4 µm   = 13 fs  deconvolved = (62) fs

LWS-20 Results: Faraday-Rotation Polarimetry: visualize e-bunch via associated B-fields change delay between pump and probe  movie of e-bunch formation observe electron acceleration on-line! 29

LWS-20 Results: Shadowgraphy Polarimetry: visualize e-bunch via associated B-fields change delay between pump and probe  movie of e-bunch formation Shadowgraphy: visualize plasma wave change electron density  change plasma wavelength observe electron acceleration on-line! 30

LWS-20 Results: Shadowgraphy Shadowgraphy: visualize plasma wave change electron density  change plasma wavelength A. Buck, M. Nicolai, K. Schmid, C.M.S. Sears, A. Sävert, J. Mikhailova, F. Krausz, MCK, L. Veisz, Nature Physics doi: 10.1038/NPHYS1942 (2011)

SUMMARY Plasma interferometry can be used to determine plasma density with high spatial resolution – a limitation exists on the minimum density x length (≈10E18 cm-3 x 1 mm ) Optical probing with fs resolution can be used to investigate ultrafast dynamics of laser plasma interactions; Probing with “ultra short” (<10fs) laser pulse can be used to unfold dynamics of laser-wakefield acceleration. Detailed analysis of diagnostic specifications requires range of specs of COMB plasmas to be defined.