X-ray bremsstrahlung and fast-ion measurements from picosecond laser-produced plasmas

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October 1977

X-RAY BREMSSTRAHLUNG AND FAST-ION MEASUREMENTS FROM PICOSECOND LASER-PRODUCED PLASMAS B. LUTHER-DAVIES Laser-Physlcs Group, Department oJ Engineering Physzcs, The Austrahan National Umverstty, Canberra, A C T 2601, A ustraha

Received 22 July 1977

Fast-ion and supratliermal electron energies have been measured from plasmas generated by 25 ps duration neodymium laser pulses focussed onto solid targets The relationship between the fast-ion energy and the energy of the suprathermal electrons in the plasma has been demonstrated and these energies have been found to increase m proportion to/o as ±o o s for targets of alummium and copper, with ! the laser intensity

1. Introduction It is well established that anomalous processes occur within laser-produced plasmas which lead to nonMaxwelhan velocity distributions of the plasma electrons. As evidence of this, several laboratories have pubhshed time and space integrated X-ray continuum spectra from such plasmas and these are not, m general, consistent with single temperature Maxwelhan electron dlstnbutmns [ 1 - 5 ] . Furthermore, studies of the plasma expansion with charged p a m c l e detectors have shown the existence of high energy fast-ions along with a less energetic background corresponding to ions from the thermahsed plasma [ 6 - 1 0 ] . The experiments have shown that the total expansion energy of these fast ions is typically 50% of the total laser energy absorped by the plasma. The appearance o f both the high-energy tall of the X-ray continuum and fast ions can be correlated with the generation of suprathermal electrons within local lzed regions of the plasma [11, 12] Recent experiments and accompanying complex computer simulations [4] suggest that the suprathermal electrons could originate from light absorptmn by electron-plasma waves in the presence of a reduced electron thermal conductwaty near the critical density region. Very large self-generated magnetic fields have been measured within laser-produced plasmas [13, 14] and these could 98

account for the reduced conductlwtles measured m several expenments [10, 15, 16]. In condmons where strongly heated electrons are prevented from penetrating the target they can dissipate a large fraction of their energy m ion blow-off. Alternatively, the dielectric swelhng of the laser field near the critical region can result in a locahsed enhancement o f the electron oscillation energy above ItS vacuum value [ 1 7 - 1 9 ] The gradient of the plasma density near the critical region and strong electrostatic coupling between the ions and electrons then allows the transfer of the electron oscillation energy to the motion of fast ions through the ponderomotwe force FNL cc (1/8~) V 2 (E 2 + H 2) [19,20] It has been shown that the pondermotlve force FNL only exceeds the thermokmetlc force, nkT, for rather high laser intensities (e g. I > 1014 W/cm 2, T e = 600 eV, X = 1 06 ~m) [19] which are generally well above the minimum intensity at which fast ions have been observed [8] Fast-ion production by this means is, therefore, unlikely at medium laser intensities Both mechanisms, however, lead to the expectation of a direct relationship between the energy of the suprathermal electrons and the kinetic energy of fast ions Several authors have pointed out that the fast ion energy from a fully stripped plasma should Increase m proportion to the atomic number Z [11,19, 21]. Some experimental evidence has been obtained from CO 2

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laser produced plasmas to support this [7]. We report here measurements of high energy X-ray and fast mn emissions from plasmas formed by irradiating various targets with 25 ps pulses from a neodymium laser at intensities between 5 × 1012 and 3 × 1015 W/cm 2 The results indicate the presence ofsuprathermal electrons with an effectwe temperature Ttt wtuch increases in proportion to I °- 35 -+0 o5 where 1 is the on-target laser flux density.

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2. Apparatus O

The laser system consisted of a passively modelocked Nd:Yag oscillator followed by a single-pulse selection system, beam shaping optics and a Nd YagGlass amplifier chain [8]. The oscillator was modelocked with Kodak 9740 dye and provided, m combination with the pulse selectmn unit, single pulses of up to an energy o f 0.5 mJ and normnal duration o f 25 ps and contrast ratio ) 1000. We were unable to monitor the duration of the Individual pulses used in the experiments but an extensive study o f the shot-toshot pulse duratmn jitter from the oscillator was performed. For this study we used a techmque similar to that described by Bechtel and Smith [22]. We monitored both the single pulse laser energy, EL, and the energy o f two-photon fluorescence, EFL,emitted from a Rhodamine 6G dye solution through which the beam was passed. For a pulse with a Gausslan profile m t~me the ratio EL/EFLis proportional to the pulse duration A histogram of the spectrum o f pulse duraUons obtained in this manner is shown in fig. 1. For our oscillator about 80% o f pulses had durations between 18 and 36 ps and 60% between 20 and 30 ps. This variation IS the major uncertainty of-+ 35% In the intensity values quoted m the following results. After amphficatlon the output energy from the laser was measured using a vacuum p h o t o d m d e which had previously been calibrated against a Sclentech 1" volume absorplng calorimeter. The maximum laser power was kept below about 40 GW in order to mmimlse the detrimental effects o f the refractive index nonh n e a n t y o f the laser glass on the beams focussing properties. Calculations showed that the systems 'Bintegral' was only 1.1 at a power o f 40 GW. The laser beam was focussed using a 75 mm F = 1 lens onto targets mounted In a chamber evacuated to

Z I

Lt_c-k !

I

20

40

PULSE

DURATION

11 60 psec

Fig. 1 Histogram showing the shot-to-shot varmtlon m the pulse duration from the mode-locked Nd-Yag oscillator. below 3 × 10 - 5 tort The targets were irradiated either from the front or rear [8] allowing various different ion probes and other detectors to be used. The probes were either deep Faraday cups biassed to - 5 0 volts or similarly biassed plane collectors screened with 200 mesh gnds. No attempt was made to reduce the levels of secondary electron emission from the collectors by using magnetic fields. Time of flight measurements were used to determine the fast-ion kinetic energies. The X-ray data was collected using a 4-channel broad-band X-ray spectrometer. Alumlnlum foils between 50 t~m and 1650 t~m thick were used to filter the X-ray radiation which was detected using 10 mm NE102A plastic scintillators and EM1 9813B photomultipliers. The overall spectral response was calculated from pubhshed X-ray data for alumxntum [23] and NE102A [23,24]. A computer code calculated the different channel responses (normalised to that of the channel with the lowest cut-off energy) as a function o f electron temperature for ldeahsed Maxwelllan electron distributions. The detectors were checked for sensitivity to light from the target by placing a 6 mm 99

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thick glass plate between the target and detectors to cut off the X-ray signal A lead colhmator was used to prevent X-rays generated by fast electrons, leaving the target and striking the chamber walls, from reaching the detectors. The focussed beam diameter at the target was measured at low power by scanning the focussed spot with a knife edge [8] and at high power from examination of the crater sizes formed in a perspex block at different power levels The spot diameter (e 1 intensity) so determined was 35 -+- 5 tim, giving peak ontarget laser flux densities of 3 -+ l 4 × 1015 W/cm 2 The measurements were made in two stages Firstly the targets were illuminated from the rear as described in ref [8] and the ton signals collected with probes which viewed along and a 90 ° to the target normal. The most accurate measurements of the fast ~on kinetic energy were made using this arrangement and the total ion flight path was between 1.15 and 1.7 metres A wide range of targets was used Including copper, aluminium, polyethylene and cadmium foils and gold or copper wires. Secondly, both fast-ions and X-ray measurements were made simultaneously In this case the targets were illuminated from the front at an angle of incidence of about 30 ° . The X-ray detector viewed the target at 90 ° to the direcuon of the incoming laser beam. A single ion probe at a distance of 20 cm viewed the target at about 40 ° to ItS normal.

3. Results The ion current traces exhibited double peaks characterlstlc of two velocity groups of expanding runs. A typical trace obtained from a 50 tim thick copper foil target is shown in fig. 2. The laser intensity was 3 × 1014 W/cm 2 and the current peaks correspond to m n energies of ~100 keV and 13 keV respectively with the maxamum detectable fast-ion energy of ~ 3 3 0 keV. In most cases it was possible to identify the peak of the fast ion signal (arrowed m fig. 2) and ItS position was used to determane the variation of fast-ion energy (EFAsT) as a function of laser intensity (/) for a wide range of target materials. The results of this study are shown in figs 3A, B, fig. 3A the variation of fast-ion energy wath laser intensity for different target materials and fig. 3B fast-ion energies as a function of Z for different laser intensities. Some features of these 100

October 1977

photo.electric sLgnal from X rays

Fig 2 A typical 1on current trace from a copper foil target Irradiated at 3 × 1014 W/cm2 The peak of the fast-ion signal is indicated with an arrow The horizontal scale is 400 ns/dlv and the target to probe distance was 0 2 m curves are of Interest. Firstly the variation ot EFAST as a function of I is shghtly different for the different target materials investigated. We find that EFAST cc i 0 35 -+0 05 for polyethylene whilst EFAST oc/0 55-+0 05 for gold. For the low Z materials the slopes of the curves in fig. 3A are slgmficantly below those reported in the CO 2 laser studies [7,9] where EFAST cci0.67. Secondly, at high laser lntensmes the fast ion energy increases linearly with Z as predicted by the simplified models where the energy of the fast ions is related to Z times the suprathermal electron energy T H. This result can be interpreted as suggesting that T H is independent of Z. At lower intensities EFAST increases sub-hnearly with Z which could be attributed either to only partial ionization of the plasmas or to a Z-dependence of T H This deduction ~s examined m more detail later. Simultaneous X-ray and fast-Ion measurements were made with 50 tim thick foils of ahiminium or copper. The X-ray cut-off energies were chosen to be 8.9, 11 5. 15 5 and 23 keV. With the copper target data from only the three highest energy channels was used because of possibility of hne radiation at ~ l 1 keV. Initial tests showed that very accurate focussing onto the targets was required to optlmise the X-ray yield m the high energy channels. Target displacement of +- 50 tim about the optimum focussing position reduced the amphtude of the X-ray signal by a factor of 2 3 and

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TARGET

October 1977

A

c/

~ 1 0 4~

I

1o3

I

1012

'I

I

1013

I

I 1015

114

ATOMIC LASER

INTENSITY

10 NUMBER

100 Z

W/CM 2

Fig. 3. The variation o f fast-ion energy with laser intensity (A) and w i t h atom]c number (B). In (B) the laser mtensltws are a, 1015 W/cm2; b, 1014 W/cm 2, c, 101 W/cm 2 "

eV

~kev

'7 '7 < "r U -01

Oe If ,g 10

20

X-RAY CUT-- OFF

IS

ENERGY

20

keV

Fxg. 4. The relative X-ray signals from the broadband X-ray spectrometer as a function of channel cut-off energy. (A) shows computer curves and sample data for an aluminmm target lrradmted at intensities of a, 9 × 1014 W/cm 2, b, 5 × 1014 W/cm 2 ; c d. 2 X 10 14 W/cm 2 F o r ( B ) the target was copper and the intensltles, e, 2.5 X 10 15 W/cm 2 ;f, 10 1S W/cm 2 ,g, 3 × 10 14 W/cm'2 .

101

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30~ AAI

.~

EFAST// Z •

Cu ~

/

XRA¥ MEASUREMENTS 10 z ~u z O z O ~k3 uJ

3

. . . . "O'J

•

ua

I I0

13

3

I I0

1 14

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3 INTENSITY

I0

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3

I0

16

W/CM 2

t.xg 5 The variation of suprathermal electron energy and fastqon energy as a function of laser mtensUy for copper and alumlnlum targets reduced the value of the measured temperature by about 30%. The computed and measured channel ratios for different cut-off frequencies for alurninium and copper targets are shown in fig. 4A and fig 4B respectxvely. The nominal laser intensity is also indicated. Some scatter between laser shots at a fixed laser energy was observed but this could be due to the pulse duration jitter already noted. For most shots the data was a good fit to the computed curves indicating that a single electron temperature could be assigned within the X-ray band being used. For a small number of shofts, however, no satisfactory single temperature could be assigned to the data, the reason for th~s being unclear at present. The values of T H deduced from the X-ray data obtained by irradiating both copper and alumlnium targets are presented as a function of laser intensity in fig 5. No significant difference was measurable between the temperature for the two materials irradiated at the same intensity. The data of fig 5 was obtamed by averaging temperature values from several laser shots at the same energy to reduce the uncertainty due to pulse duration jitter Also shown In fig. 5 is the intensity dependence measured for the fast-ion energy, EF AST / Z , for copper and aluminium. The data from both sets of measurements IS m good agreement under102

hning the relationship between fast Ion emission and suprathermal electron generatxon. Over about a two decade increase m laser Intensity the hot electron temperature is deduced to increase in proportion to l 0 35 +-0 05

4. Discussion These results confirm the relatmnshlp between fastion emission and suprathermal electron production within laser-produced plasmas In this respect they are In agreement with those presented by Fabre et al. [25] who studied fast-Ion and X-ray emission from nanosecond pulse CO 2 laser produced plasmas. They differ in that the intensity dependence o f the suprathermal electron energy has been found to be different from that deduced from the fast-ion and X-ray measurements using CO 2 lasers [7,9, 25]. The values of T H deduced from these measurements are in fair agreement wlth those from other neodymium laser experiments. For example, Rlpln et al. [3] reported X-ray temperatures ~ 1 0 keV for CH 2 and Al plasmas Irradiated at ~1016 W/cm 2 m either 25 or 250 psec pulses. Haas et al. [4] have also published high energy X-ray spectra from parylene disc irradiated by 5 0 - 1 5 0 ps neodymium laser pulses from which Tft can be deduced to be about

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10 keVat I = 1015 W/cm 2 and about 30 keVat 1016 W/cm 2 At 1015 W/cm 2 these latter results are within 20% of those reported here. Extensive computer modelling is required to determine a theoretical prediction of the dependence of suprathermal electron energy on laser intensity. Without such facilities some qualitative insight into the possible Interaction processes can be obtained using much simplified analytic models. The absence of an observable threshold in the range 1012-1014 W/era 2 for fast-ion and, hence, suprathermal electron generation suggests resonant absorption as the mechanism most likely to be involved in their production. In that case the average suprathermal electron energy (e) can be written as

(e) = (rneCOoPA L/Nc) 1/2

(1)

where PA is the absorped laser flux, L the plasma density scale length, and N c the critical density [26]. In this equation both PA and L can be intensity dependent Under the assumption that the plasma density scale length and absorption coefficmnt are constant then (e) scales at I 1/2. Accurate measurements of plasma absorption coefficients are not readily available in the intensity range of interest, however, data from parylene disc experiments [4] indicate that the absorption coefficient is nearly independent of intensity in the range 1015-1017 W/cm 2. At lower intensities where inverse Bremsstrahlung plays a bigger part in the absorption process and increases the total plasma absorption, experimental values will not necessarily correspond to PA m eq. (1). Theoretical models of resonant absorptmn also indicate that considerable locahsed density profile steepening can occur during the laser pulse. This is due principally to ponderomotire forces [27, 28] acting on the plasma due to the locally enhanced electric field of the beam near the critical surface. Such forces tend to decrease the density scale length L by ejecting the plasma to the regmns of lower electric field away from the critical surface. The importance of such profile modification has been demonstrated in simulations of resonance absorption by Estabrook, Valeo and Kruer [28] where local density jumps AN/Ncr ~ 1 in a few tens of electron Debye lengths have been observed With increasing laser intensity the scale length L is expected to decrease by this mechanism leading to an intensity dependence of the average electron energy (e) below I 1/2 predicted

October 1977

for constant scale length L by eq. (1). Although the X-ray measurements from aluminium and copper targets supported by the fast-Ion data indicate that the suprathermal electron energy is independent of Z, this deduction IS rather surprising and the fast-Ion data IS probably misleading in this respect. If we conclude that Tft is independent of Z then at high intensmes this implies that even the hlgh-Z plasmas are fully ionized (see fig. 3b). This deduction can be examined using the coronal model [29] to calculate the relative populations of the different ionization states for several materials, together with the approximate ionization times for those states. For the calculations it is necessary to have a value for the plasma electron temperature T e which was not measured in these experiments We, therefore, used T e = 200 eV which lS consistent with measurements under similar conditions by other workers [ 3 0 - 3 2 ] . This temperature is insufficient to fully strip ions above approximately Z = 12 in steady-state conditions Ionization tnnes can be calculated using the expression r z N e = [S(Z+ 1) + ~(Z)] -1

(2)

where r z is the ionization plasma a plasma of electron density Are, S(Z+I) is the ionization coefficient between levels Z and Z+I and c~(Z) is the recombination coefficient between levels Z+I and Z [331. Specific examples indicate that r z is only short compared with the laser pulse duration for weakly Ionized hlgh-Z plasmas. For example with N e = 10 21 cm -3 the transition Cu 20+ t o C u 21+ gives r z ~ 4 ns w h i l s t for Cu 18+ to Cu 19+, r z = 30 ps. For hIgh-Z materials, therefore, ionization states up to 20 + are the maximum expected from the coronal model. Investigations of the charge states in expanding plasma of gold and carbon using a parallel plate electrostatic analyser give support to this deduction. The plasma temperature was sufficient to strip carbon to C 5+ [34] but only partially ionize gold to Au 15+. Since the results from alumlnlum and copper imply that the fast-ion energy and suprathermal electron energy can be related by the ionic charge, a partial stripping of the high-Z materials together with the nearly linear increase in fast-ion energy with Z at high intensmes observed here suggests that T H increases with Z. Preliminary measurements of T n for gold have been made which give values about two to three times greater than those for copper and alumInIum. However, in comparison with the data for copper and alu103

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m l n i u m , t h a t f r o m gold s h o w e d only a small p e r c e n t age o f s h o t s for w h i c h a single e l e c t r o n t e m p e r a t u r e c o u l d be assigned a n d f u r t h e r m e a s u r e m e n t s over a wider b a n d o f X-ray energies will be n e e d e d to clarify this result In c o n c l u s i o n we have d e m o n s t r a t e d the r e l a t i o n b e t w e e n fast-ion a n d s u p r a t h e r m a l e l e c t r o n energies for targets o f a l u m l n t u l n a n d c o p p e r a n d find t h a t for i n t e n s i t i e s b e t w e e n a b o u t 1013 a n d 1015 W / c m 2 these energies increase in p r o p o r t i o n t o / 0 35 _+0.05. This mt e n s i t y d e p e n d e n c e is c o n s i s t e n t w i t h e l e c t r o n h e a t i n g b y r e s o n a n t a b s o r p t i o n in the p r e s e n c e o f an i n t e n s i t y d e p e n d e n t plasma d e n s i t y scale length. P r e l i m i n a r y results suggest t h a t t h e s u p r a t h e r m a l e l e c t r o n t e m p e r a ture increases w i t h h t g h - Z materials a n d this is t h e subject o f f u r t h e r i n v e s t i g a t i o n .

References [i] V.W Shvmsky, HN. K o r n b l u m a n d H D Shay, J A P . 46 (1975) 1973 [2] J F. Kephart, R.P. Godwin and G H McCall, A P L 25 (1974) 108 [3] B H R l p a n e t a l , P h y s Rev Letters 34 (1975) 1313. [4] R.A. H a a s e t a l , P h y s Flmds 20 (1977) 322. [5] P. Mulser, R. Slgel and S Wltkowskl, Phys. Rep 3C (1973) 187. [6] C Yamanaka et al, Phys Rev A6 (1972) 2335 [7] A.W Ehler, J.A P. 46 (1975) 2464 [8] B Luther-Davies and J L Hughes, Optacs Comm 18 (1976) 351. [9] J Martmeau, M. Rabeau, J.L Bocher, J P. Ehe and C Patou, Optics Comm 18 (1976) 347 [10] J S. Pearlman and J P Anthes, A.P L 27 (1975) 581. [11] R.L Morse a n d C W Nlelson, Phys Fluids 16 (1973) 909

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[121 R.C Malone, R.L McCrory and R L Morse, Phys Rev Letters 34 (1975) 721 [13] J A, S t a m p e r e t a l , P h y s Rev Letters 26 (1971) 1012 [14] J A Stamper and BH Rlpm, Phys Rev Letters 34 (1975) 138 [151 B. Yaakobl and T C Brlstow, Phys Rev Letters 38 (1977) 350. [16] WC M e a d e t a l , P h y s Rev Letters 37 (1976) 489 [17] H. Hora, Phys Fhuds12 (1969) 182 [18] J D L l n d l a n d P K Kaw, Phys Fluids 14(1971) 371 [19] H ttora, Laser plasmas and nuclear energy (Plenum Press, New York, 1975) p 52 [20] D B a b o n e a u e t a l , P h y s . Letters 57A (1976) 247 [21] K l t o h a n d S Inoue, Phys Rev Letters 37 (1976)503 [22] J ft Bechtel a n d W L Smlth, Phys Letters 55A (1975) 2O3 [23] C.M Davlsson, c~,v3and "y-ray spectroscopy, ed K Slegbahn (North-Holland, Amsterdam, 1965) p 830, The Encyclopedia of X-rays and gamma rays, ed G.L Clark (Reinhold Pubhshmg Co , N Y , 1963) [24] J H Adlam, J C Taylor, Culham Research Group Report CLM-R81 (1968) [25] E Fabre, C Garban, C. Popovlcs, A. Poquerusse, C. Stenz and J Vlrmont, Proc. IXth Intern. Conf on Quantum electromcs, Amsterdam, June 1976, paper T8 [26] J P. Freldberg, R W Mitchell, R L Morse and L 1 Rudsmskl, Phys Rev Letters 28 (1972) 795 [27] D W l'orslund, J.M. Kmdel, K Lee, E L Llndman and R L Morse, Phys Rev A l l (1975) 679 [28] K G Estabrook, E J. Valeo and W.L Kruer, Phys Fluids 18 (1975) 1151. [29] C Jordan, Mon. Not R Astr. Soc 142 (1969) 501 [30] H. Salzmann, J Appl Phys. 44 (1973) 113 [31] J N Ohlson and C W. Mendel, J Appl Phys 46 (1975) 4407 [32] P G. Burkhalter et al, N.R L Memorandum Report 3315 (1976) [33] R.W P McWhtrter, Plasma daagnostlc techmques, eds R.H Huddlestone and S.L Leonard (Academic Press, New York, 1965). [34] G Tallents, private commumcatlon.