Laser and Particle Beams (1998), vol. 16, no. 3, pp. 431-443 431Printed in the United States of America

Some studies on picosecond laser producedplasma expanding across a uniform

external magnetic field

; By V.N. RAI, M. SHUKLA, AND H.C. PANTLaser Plasma Laboratory, Centre for Advanced Technology, P.O. CAT, Indore 452 013, India

(Received 2 September 1997; Accepted 16 March 1998)

Some characteristics of the picosecond laser produced plasma expanding across an externallyapplied magnetic field (0.6 T) have been reported. Two to three times enhancement in X-rayemission from copper plasma has been observed for the laser intensity range -5 X 10 II to 5 X

1012 W/cm2. The X-ray yield has been found to increase with an increase in the magnetic fieldintensity. Enhancement in X-ray emission is correlated with confinement of expanding plasmaeither in external magnetic field or in high ambient gas pressure. Generation of some high-frequency instability and fast ions was also observed in the plasma along with bouncing ofplasma near the fJ = 1 surface where kinetic pressure of plasma equals magnetic pressure. .

1. Introduction

Laser produced plasma has been extensively studied using laser pulses of various time du-ration (ns-fs) providing irradiances ranging from 1012 to 1018 W/cm2 (Cairns & Sanderson1980; Radziemski & Cramers 1989). There is great interest in the generation of short timeduration intense and small size X-ray source for applications such as plasma diagnostics inlaser produced plasma and inertial confinement fusion (ICF) experiments, X-ray lithography,X-ray microscopy, and EXAFS (Radziemski & Cramers 1989), and so forth. Several tech-niques have been reported in the literature (Balmer & Donaldson 1977; Richardson et at. 1980;Yaakobi et at. 1981; Balmer et at. 1990) to enhance the X-ray emission. Out of these experi-ments, investigation of laser produced plasma expanding across a static or DC magnetic fieldis interesting (Suckewer & Fishman 1980; Suckewer et at. 1985; Enright & Burnett 1986)because magnetic field is one of the means to affect dynamics, ionization, and optical charac-teristics of the expanding plasma. This scheme has also been found useful in increasing the gainof the lasing medium of X-ray laser (Suckewer & Fishman 1980; Suckewer etat. 1985) whenoperated in recombination regime as a result of increase in particle confinement, because inthis case particle confinement time remains much larger than the electron temperature decaytime and the plasma is cooled through the radiation losses. In these experiments strong sole-noidal magnetic field is applied along the direction of plasma expansion or plasma column. Anenhancement of -100 in stimulated emission (along magnetic field) over spontaneous emis-sion (perpendicular to magnetic field) of C VI 182 A line has been measured in the presence of90 kG magnetic field. However, no information is available about the emission without andwith the magnetic field. Enhancement in UV and visible emission from beryllium plasma in thepresence of magnetic field have also been reported (Begimaculov et at. 1992). Enright andBurnett (1986) have reported an enhancement in hard X rays along with generation of hotelectrons using CO2 laser with 100 kG confining magnetic field. Generally in the case of steepdensity gradient (Ln = 2-3 jLm), collisionless resonance absorption, or at high laser irradi-

@ 1998 Cambridge University Press 0263-0346/98 $12.50I

432 ~N. Rai et at.

ances, laser energy is deposited into a hot electron distribution at the critical density surface(Radziemski & Cramers 1989). These electrons distribute their energy in two ways. They caneither transport their energy into target interior and form a thermal plasma or they can accel-erate ions through the potential sheath formed as a result of ambipolar diffusion of fast elec-trons. Generation of hot electrons is found correlated with the observation of hard X ray andfast ions from laser produced plasma (Eidman et at. 1984).

The main aim of the present experiment was to study the enhancement in X-ray emissionalong with its correlation with plasma dynamics using comparatively low intensity (5 X 1012W/cm2) from a picosecond time duration laser and external magnetic field (0.6 T) perpendic-ular to the laser axis. The effect of ambient chamber pressure on X-ray emission in the absenceand presence of magnetic field is also discussed.

2. Experiments

The experimental setup used in the present study utilized a second harmonic radiation(0.53 .um) of a Nd:YAG laser delivering up to 15 mJ energy in TSH -25 ps. The laser beamwas focused onto a flat massive polished copper target using a spherical lens of 30 cm focallength whereas laser energy was changed using neutral density filters. Thick planar targets ofcopper, aluminum, and gold were used to form the plasma in a vacuum chamber evacuated at-10-5 Torr pressure. The X rays emitted from laser produced plasma were monitored using amultichannel vacuum photodiode (Rai et at. 1995a) having a thin zapon (4 .um) and 12-.um-thick aluminum filter. X-ray detectors were kept at 450 with respect to the target normal whereasLangmuir probes were kept at -100 (just below the laser entrance) and 450 with respect to thetarget normal at a radial distance of 5 and 17 cm respectively to monitor the ion saturationcurrent (time of flight). The electrical signals from X-ray vacuum photodiode and Langmuirprobes were recorded using a 100 MHz L&T Gould model 7074 digital storage oscilloscope(400 MS/s). An X-ray pinhole camera was used to image the spatial X-ray emission from theplasma in the absence and presence of magnetic field. An X-ray streak camera (Rai et at.1995b) was also used to find the temporal information about X -ray emission from the plasma.Zapon foil (4.um) was used as a filter that transmits the soft as well as high energy X rays. Allpinhole and streak images were recorded at 900 (side on) from the direction of laser axis. Aphosphor screen and image intensifier combination was used as detector in the image plane ofthe pinhole camera (Rai et at. 1996). Final intensified images from pinhole and streak cameraswere recorded using a CCD camera, and images were processed to find the isointensity contourof the pinhole image and the temporal intensity profile of the streak image respectively. Twostrong bar magnets (ferrite) of 10 X 10 cross-sectional area kept at 5 mm separation were usedto generate uniform magnetic field of 0.6 T between the poles. Both the target and the barmagnets were held inside the plasma chamber with the help of two independent manual ma-nipulators such that in one case the target was in between the magnetic poles (figure 1a) and inthe other case the target was touching the magnetic poles (figure 1 b) such that the position ofthe target was changed without affecting the magnetic field at the location of plasma formation,so as to take each shot at a fresh location. Laser plasma produced in the arrangement shown infigures 1a and 1b expands -3 and 10 mm respectively in the uniform magnetic field of 0.6 T.But as the plasma comes out of the magnetic poles it feels decreasing magnetic field whichdecays to zero at a distance of 5-6 cm. To avoid the possibility of X-ray emission from magnetpoles due to plasma bombardment, a polymer tape was wrapped on it. There was an arrange-ment to pull the magnet in such a way that it remains inside the chamber without affectingsignificantly the expanding plasma. However a residual magnetic field of -100 G was mea-sured in this case also at the location of plasma formation, when the bar magnets were signif-icantly away from the plasma.

-

Laser produced plasma in magnetic field 433

10rmn(A) 5mm 6KG -

5&0 I 3'G ' 1'G ' ,

D~~,BAR MAGNET ~ D

~ -LASER ~ -LASER

D D(8) (C)

FIGURE 1. Arrangement of target and magnet in vacuum chamber.

3. Experimental results

3.1. Study o/X-ray emission

The X rays emitted from copper plasma were detected using a multichannel vacuum photo-diode array (Rai et al. 1995a) and were recorded on a digital storage oscilloscope in the pres~ence and absence of magnetic field as well as with increasing laser intensity while keeping allthe other parameters constant. Figure 2a shows the variation of X-ray intensity with laserintensity at 0.01 and 0.6 T magnetic field. It was observed that the X-ray signals from copperplasma were enhanced 2-3 times when the magnetic field was increased from 0.1 to 0.6 T.However no change was observed in X-ray intensity in the absence or presence of 0.01 Tmagnetic field. An enhancement of 3-4 times in the case of gold plasma and :52 times inaluminum plasma was observed. In this case X-ray detector with zapon filter was sensitive forsoft as well as hard X-ray energy. Figure 2b shows variation of X-ray emission with laserintensity when the detector had a 12-JLm-thick aluminum filter that is transparent mainly toX ray with energy >2 keY. In this case also enhancement in X-ray emission is 2-3 times in thepresence of 0.6 T than 0.01 T magnetic field. However 4-5 times enhancement in X-ray emis-sion was found toward higher intensity (5 X 1012 W/cm2) of the laser (figure 2b). It was notpossible to go beyond this intensity range due to experimental limitations. Our observations arein qualitative agreement with Enright and Burnett (1986), who have reported 1.5 and 2 timesenhancement in X-ray emission at 0.6 T magnetic field for X-ray energy 100 and 200 keYrespectively. They have used carbon dioxide laser for generating plasma at high intensity -1014W/cm2 which is why emission of high energy X-rays is expected. The scaling of X-ray emis-sion with laser intensity follows the power law variation as Ix CK (IL)a with a = 0.5 atB = 0.6 T,

which is much smaller in comparison to a -1.5 measured in the absence of magnetic field.Generally the value of a has been reported to be ranging from 1.5 to 2.5 in the absence ofmagnetic field (Bleach & Nagel 1978; Rai et al. 1995b). Actually three types of slopes (powerlaw index a) were observed in X-ray emission v/s laser intensity variation obtained experi-mentally (figures 2a and 2b), which are -1.5 in the absence of magnetic field, -1.5 and ,0.5in the presence of 0.01 T magnetic field, and -0.5 in the presence of 0.6 T magnetic field.These observations indicate that at the magnetic field of 0.1 T a new decreased slope (a -0.5)

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434 ~N. Rai et al.

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FIGURE 2. Variation of X-ray intensity with laser intensity: (a) photodiode signal with 4-p,m Zapon filter;(b) photodiode signal with 12-p,m aluminum filter.

develops after a certain laser intensity. However at higher magnetic field of 0.6 T only ont\ decreased slope (a -0.5) is seen for all the experimental range of laser intensity. It seems thai

threshold intensity is very small (out of experimental range) in the case of 0.6 T magnetic fieldIt also appears that the threshold intensity for change in slope is strongly dependent on thtstrength of the magnetic field, which decreases with an increase in the magnetic field strengthDecrease in slope at higher magnetic field indicates that the absorbed laser energy is being 10SI

--

Laser produced plasma in magnetic field 435

through a new channel that is dependent on the strength of magnetic field as well as laserintensity. This phenomenon of decrease in the slope has been observed whenever high intensitylaser interacts with the plasma and generates fast electrons as well as hard X ray. Generation ofsome parametric instabilities has also been observed at higher laser intensity (Cairns & San-derson 1980; Radziemski & Cramer 1989). The threshold seems to be correlated with thestart-up of high-frequency oscillation in ion current when the laser produced plasma is ex-panding across the magnetic field. According to Chang and Hashmi (1977) some regular os-cillations (1 MHz) have been observed in ion current at low magnetic field (B = 170 G) whenN oc f3 > 1 whereas for N oc f3 < 1 oscillations became random and at irregular time intervals.

The present experimental observation at 100 G magnetic field and 8 X lOll W/cm2 intensity(threshold) is similar to the first case of N > 1. This supports the idea that change in the slopeis correlated with the onset of instability in the plasma. Presence of instabilities in the plasmaenhances the particle loss as well as loss in energy content of the plasma as has been reportedearlier in the case of magnetically confined devices (Liewer 1985). Even as a result of waveparticle interaction particle acceleration can take place. Phenomena like particle accelerationand hard X ray generation have been observed in laser plasma interaction taking place at highlaser intensity> 1014 W/cm2 (Eidman et al. 1984). The present experimental results indicatethat an interaction of picosecond laser light (-5 X 1012 W/cm2) with the plasma expanding inthe presence of magnetic field seems to produce similar results to those by high intensity laser.This idea has been supported on the basis of two observations. The first one is the large en-hancement in hard X rays in the energy range E > 2keV when the laser intensity was in thehigher intensity side of the experimental range (1012 to 5 X 1012 W/cm2). Second, some fastion pulsation was observed in the ion current in the presence of magnetic field at comparativelyhigh laser intensity.

Figure 3 shows the digitized image of time integrated X-ray pinhole pictures of the laserproduced plasma expanding in vacuum with and without the magnetic field. Expansion of theplasma without the magnetic field is nearly spherical in nature. The spatial extent of the X-rayemission region is measured up to -450 ,urn from the target surface. The hottest portion of theplasma (highest brightness spot) in the center spans from -100 to 200,um (figure 3a). Butwhen the plasma was allowed to expand across a 0.6 T magnetic field it shows distortion ateach isointensity contour as is shown in figure 3b. Distortion in the smooth expansion ofplasma boundary seems to be due to generation of some kinds of instabilities as a result ofdeceleration in plasma expansion in the presence of magnetic field. Effect of magnetic field inthe form of plasma distortion can be seen even in the hottest portion. In this experiment ion andelectron Larmor radius were found -3 and 0.05 mm respectively. Ion Larmor radius was largerthan the density gradient scale length CsT -2-3 ,urn, which shows that ions were effectively

a F+-- b

-..c-cc

FIGURE 3. Digitized X-ray pinhole image of laser produced plasma: (a) expanding in vacuum; (b) ex-panding across magnetic field.

--'-"---

436 ~N. Rai et al.

unmagnetized in comparison to electrons. In this condition generation of Rayleigh-Taylor orfinite Larmor radius instabilities is expected as reported earlier (Ripin et al. 1987). Howeverpresence of Kelvin-Helmholtz instability due to electron velocity shear (as a result of com-bined effect of self-generated spontaneous magnetic field and external magnetic field) also cannot be ruled out (Sydora et al. 1983). The spatial extent of X-ray emission from target surfacein the presence of magnetic field is limited to -350 JLm across the magnetic field. However nosignificant change was found in plasma size along the magnetic field. These pictures indicatethat plasma is becoming confined in the presence of magnetic field, which is expected and is inagreement with the results of Pisarczyk et al. (1992) where magnetic field was applied alongthe direction of plasma expansion and decrease in plasma size was recorded perpendicular tothe magnetic field. An increase in X -ray emission is expected due to increase in plasma densityas a result of decrease in the plasma expansion velocity (figure 3) because X -ray intensities dueto bremsstrahlung, recombination, or line radiation all are directly proportional to square of

plasma density.Figure 4 shows the time dependent X-ray intensity profile emitted from the laser produced

plasma in the absence and presence of magnetic field. These observations were recorded witha 4-JLm Zapon filter in front of photocathode of X-ray streak camera. It was noticed that X.-rayemission remains for nearly the same time duration T x -1.5 ns in both cases. However the onlydifference in the intensity profile is that it broadens near the peak when it starts decaying. X-rayemission peaks between 400 and 500 ps in both cases whereas it increases after the peak in thecase when magnetic field was present in comparison to the absence of magnetic field. Howevertotal time duration of X-ray emission remains the same. This indicates that an increase in X-rayintensity after 500 ps seems to be due to increase in plasma density at that time as a result ofplasma confinement in the presence of magnetic field, which is in agreement with the obser-vation of the X-ray pinhole camera result, which shows a decrease in the size of X-ray emittingplume as a result of magnetic confinement. We can infer from the streak camera measurementthat plasma expands nearly 400 to 500 ps smoothly and after this it starts feeling the deceler-ation due to presence of magnetic field.

Figure 5a shows the variation in X-ray emission from laser produced plasma as the ambientpressure of the plasma chamber increases from -10-5 to 10-1 Torr of normal air. It wasnoticed that X-ray emission first decreases and then increases on both the channels of photo-diode as the chamber pressure increases from -10-5 to 10-1 Torr. Similar observations havebeen reported earlier in the case of optical radiation from carbon plasma (Diwedi & Thareja1995). Measurement of ion current using Langmuir probe with an increase in chamber pressureshows a small increase first (from 10-5 to 10-4 Torr) followed by a gradual decrease. However,ion current signal was not measurable at 10-1 Torr using the probe located even at 5 cmdistance from the target. Initial increase in ion current with chamber pressure may be either dueto an increase in neutral pressure and subsequent photoionization of neutrals due to ultravioletand X rays produced from plasma or due to electron impact ionization with increased numberof neutrals in plasma (Goldston & Rutherford 1995) whereas a further increase in pressurebeyond 10-4 Torr increases the probability of radiative as well as three-body recombinationbecause low-temperature plasma is dominated by electron-ion collisional radiative recombi-nation. It has been reported that radiative recombination is larger than three-body recombina-tion at lower density in the case of coronal equilibrium in which electron impact ionization andradiative recombination are in balance (Goldston & Rutherford 1995). It seems that this in-crease in X-ray emission with increase in ambient pressure beyond 10-4 Torr may be due toenhanced radiative recombination whereas decrease in ion current seems to be due to thecombined effect of radiative as well as three-body recombination. However, the role of chargeexchange process at high chamber pressure can not be ruled out as it plays an important role inpopulation inversion in X-ray laser (Suckewer & Fishman 1980). A drastic decrease in X-ray

Laser produced plasma in magnetic field 437

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FIGURE 4. Temporal behavior of X-ray emission: (a) in the absence of magnetic field; (b) in the presenceof magnetic field.

emission at very high pressure (> 10-1 Torr) was observed that may be due to increase in theabsorption of X ray as a result of increased density of background neutrals. It was noted thatexpansion velocity of the plasma also decreases slightly with an increase in chamber pressure.Figure 5b shows the variation in X-ray intensity when the ambient pressure was increasedwhile the plasma was expanding across the magnetic field. In this case X-ray emission wasmaximum between 10-5 and 10-4 Torr pressure, which started decreasing as the pressurestarted increasing. This observation can be explained on the basis that the presence of 0.6 Tmagnetic field slows down the expansion of plasma, which increases the effective plasmadensity in the emission zone as is indicated by the X-ray streak camera record. Due to increasein effective density, X-ray emission increases through all the processes, namely, bremsstrah-lung, radiative recombination, and line radiation, because each one has direct dependence onplasma density (Griem 1964; Huddlestone & Leonard 1965). However, an increase in ambient

438 \l:N. Rai et al.

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FIGURE 5. Variation of X-ray emission with change in the ambient pressure of plasma chamber: (a) in theabsence of magnetic field; (b) in the presence of magnetic field.

pressure in the presence of 0.6 T magnetic field further increases the plasma density, andprobably it starts collisional cooling of plasma (Diwedi & Thareja 1995) or X-ray absorptionin the background gas. During this observation ion current decayed comparatively very fast inthe presence of magnetic field when ambient pressure of the chamber was increased beyond10-3 Torr.

r ,"

Laser produced plasma in magnetic field 439

3.2. Plasma expansion across the magnetic field

Figure 6a shows the ion current measured in the absence of magnetic field by a Langmuirprobe located at -15 cm radial distance from the target and at 450 from the target normal.Target was kept in between the magnet as shown in figure 1 b. The expansion velocity of ionwas calculated as -1.4 X 107 cm/s at the peak of the ion current. This measurement was

recorded on the laser intensity of -1012 W/cm2. Signal on the probe due to X ray was consid-ered as reference in calculating the time of flight of ions. Figure 6b shows the ion saturationcurrent when plasma was expanding across a uniform magnetic field (0.6 T). Two main peaksalong with some high-frequency oscillations superimposed on it are seen in the ion current. Itwas noted that amplitude of the ion current pulse goes down in the presence of magnetic fieldalong with an increase in its full width at half maximum (FWHM). The expansion velocity inthe case of the first peak comes out to be -1.13 X 107 cm/s in comparison to -1.42 X 106 cm/s

a b

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X-AXIS -125 ns/Div

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FIGURE 6. Oscillogram of Langmuir probe signal at r = 15 cm, (J = 45°: (a) in the absence of magneticfield; (b) in the presence of magnetic field (when the target was in the center); (c) in the presence ofmagnetic field (when target was at one end of magnet and probe was at r = 5 cm and (J = 10° below laserbeam).

~..II'III_II -

440 ~N. Rai et al.

for the second peak. The second peak in the ion current in figure 6b seems to be due to thesecond bounce taken by ions on the plasma magnetic field interface as a result of finite plasmaresistance as has been observed and reported earlier theoretically (Bhadra 1968) as well asexperimentally using gated optical diagnostics (Tuckfield & Schwirzke 1969). The FWHM ofcurrent of ions expanding across the magnetic field increases due to these bounces. The ex-pansion velocity goes down by 20% during the first peak or bounce whereas in the case of thesecond peak, velocity remains only 17% of the expansion velocity measured in the absence ofmagnetic field. This drastic decrease in expansion velocity during the second peak seems to bedue to cooling effect in the plasma as a result of emission and increased plasma collision. In thiscase plasma expands only -3 mrn in uniform magnetic field and after that magnetic fielddecreases very fast with distance. Ion expansion will be more after first bounce in lower mag-netic field, which may lead to a large time delay between first and second bounce. Figure 6cshows the ion current measured when the plasma expands -10 mm (figure lc) in the uniformmagnetic field. In this case the probe was kept at 5 cm from the target surface but at -10° justbelow the direction of laser. Three bounces of the expanding plasma are seen with decreasingamplitude. Here again the expansion velocity of the first peak is less than the measured inabsence of magnetic field. Similar variations in ion current were recorded at 45° from the targetnormal. The frequency of bounce (large amplitude oscillations) was calculated -4 MHz whereashigh-frequency (-100 MHz) oscillations were superimposed on it. Decrease in amplitude ofion current was noted in the presence of magnetic field which was independent of target andmagnetic field arrangement (figure 1). Decrease in ion current seems to be due to confinementof plasma. However oscillations were more erratic in the case when ion current was recordedusing a probe located at 45°, which seems to be due to gradient in magnetic field seen by plasmaduring its expansion at 45°. These observations indicate that magnetic field lines oscillateunder the effect of plasma pressure and restoring force due to magnetic pressure. Initiallysmooth expansion takes place till the fJ = 1 surface, where plasma pressure is equal to the

magnetic pressure. These observations are in close agreement with the theory given by Bhadra(1968). High-frequency oscillations superimposed on the ion current are due to generation ofsome kind of instability due to plasma deceleration in magnetic field which are observed in theX-ray pinhole image also in the form of distortion in isointensity contour. A detailed study ofoscillation modes in the plasma expanding across the magnetic field will be reported sepa-rately. However, these results indicate that an enhancement in X-ray emission is correlatedwith the decrease in the expansion velocity of ions in the presence of magnetic field. Thisenhancement in X-ray emission during deceleration of ions may be due to conversion of kineticenergy of ions into thermal energy as a result of relaxation of compressed magnetic field as hasbeen reported earlier (Dawson 1964; Bhadra 1968). It could also be due to an increase inradiative or three-body recombination away from the target surface where plasma temperatureis low and plasma density goes up as a result of increased particle confinement in the emissionregion. However both may be playing a role together in this process. The role of densityconfinement in X-ray enhancement is analyzed in the next section which seems to be playinga dominant role.

4. Discussion

4.1. Plasma dynamics

The total number of atoms ablated from the surface was calculated to be -1.24 X 1013 forincident intensity of laser -5 X 1012 W/cm2. Considering that atoms are Z -10 times ionized(kTe -180 eV) the total number of plasma particles was obtained as -1.36 X 1014. Only Ep-4.4 mJ energy remains in the plasma out of EL -10 mJ incident energy. Ep was calculatedconsidering energy loss from plasma as Eref. -2.5 mJ, Erad. -1 mJ (Eidman & Schwanda

-.-Laser produced plasma in magnetic field 441

1991), and Eion. -2.06 mJ, which provides energy per particle as -204 eV. The measuredplasma temperature using K-edge spectrometer comes out to be -180 eV whereas temperaturecalculated using asymptotic expansion velocity comes out to be

MV2To = s-cz-+i) = 234 eV (1)

whereMi-63 X 1.67 X 10-24 gisthemeanionmass and V1-l.4 X 107 cm/s.AIl three valuesof temperatures are in close agreement. High-temperature plasma expands across the magneticfield where magnetic pressure acts as a restoring force and stops the plasma expansion. Initiallysmooth expansion takes place when fJ » 1, but expansion stops near the fJ = 1 surface at a

distance of bounce radius rb' As discussed in the theoretical paper on the expansion of a resis-tive plasmoid in magnetic field by Bhadra (1968), an energy integral can be obtained fromOhms' law, the momentum and energy equation. Neglecting the resistivity and skin depth termone can write the equation as

B2/3(rt -rJ) = 3/2(Ne + Ni)kTo.rJ(I/rJ -l/rt) + 1/2 MV2. (2)

Assuming that at to when plasma becomes transparent

MV2/2« 3/2 (Ne + Ni)kTo

and

rb » ro (plasma radius at to).

An expression for the bounce radius can be written as

rb = [9/2.NkTo/B2]1/3 = 1698 X 10-4 cm, (3)

where N -1.36 X 1014 is the total number of plasma particles present in the plasmoid andkTo -180 eV. However the bounce radius was found as -1765 JLm when kTo was replacedby the energy content of plasma as 4.4 mI. In both the processes bounce radius comes outto be nearly the same. If we consider that plasma expands with acoustic velocity Cs =[(Z + l)kTo/Mi] 1/2 -5.6 X 106 cm/s, then bounce time T -rb/Cs -30 ns is expected. Plasma

deceleration was obtained as 4.67 X 1014 cm/s2 using simple equation of motion, which clearlyindicates that after Tx -1.5 ns plasma expansion velocity goes down by -5% of initial expan-sion velocity. Time duration of X-ray emission was found as Tx -1.5 ns when a -4-JLm Zaponfilter was used in front of the streak camera photocathode (figure 4). This indicates that X-rayemission exists even when plasma starts feeling the effect of magnetic field in the form ofdecrease in expansion velocity that is T x > TB -500 ps. TB is the characteristic time whenmagnetic field starts affecting the plasma expansion and shows decrease in expansion velocityby 1.6%. Instead of one bounce there will be many bounces but the radius of the second bouncewill be less due to decrease in plasma temperature or loss in energy content of plasma. Theenergy loss from the plasma in the form of radiation and particle losses parallel and perhaps byinstabilities across the magnetic field seems to act like a damping mechanism on the periodicbehavior of plasma expanding in the magnetic field. However bounce radius will be constantif one considers that plasma has infinite conductivity. In this case there will not be any loss inenergy (damping in ion current) during relaxation of distorted magnetic field.

4.2. Modelfor X-ray enhancement

A simple analysis was performed to understand the effect of an increase in density in theX-ray emission region as a result of deceleration in ion expansion velocity. The X-ray emis-sions from such type of plasmas are dominated by the bremsstrahlung, recombination, and line

I.

-

442 ~N. Rai et a/.

radiation. In all three cases X -ray emission is proportional to the square of the plasma density(nen;, where ne == n;) as well as its volume. If we consider that for the same laser intensity the

coronal plasma generated and expanding in the presence and absence of magnetic field willhave nearly close plasma parameter such as plasma density, temperature, and charge state Z. Inthis case total amount of X-ray emission seems to be proportional to the volume and square ofthe density of the emitting coronal plasma. If we consider V} and V2 as the average expansionvelocity and T} and T2 the X-ray emission time in the absence and presence of magnetic fieldrespectively, then with nearly spherical plasma expansion as is shown in pinhole pictures(figure 3) the plasma will expand a distance given by VITI and V2T2 respectively. The volumeof the hemispherical coronal plasma can be considered as 2/31T(V} T})3 and 2/31T(V2TJ3 re-spectively, where V} T} and V2T2 are considered as radius of the plasma sphere. The mass ab-lation rate (ni) per unit area per unit time is considered to be equal in both cases because thelaser intensity is same. Here the total mass ablated can be given by M = ni1Tr2TL, where TL is

laser time duration. Density of the coronal plasma in the absence and presence of magneticfield can be given by the ratio of mass ablated and plasma volume. Since the total X-rayemission is proportional to the plasma volume and square of the plasma density, therefore theratio of X-ray intensity emitted from plasma with (XJ and without magnetic field (X}) will be

given by 1

X2/XI = [VITI/V2T2]3, (4)

where VI TI -450 JLm and V2T2 -350 JLm are nothing but the size of the X-ray emitting plumerecorded using a pinhole camera in the absence and presence of magnetic field which providesX2/XI -2.13. With the help of the measured value of VI = 1.4 X 107 cm/s, V2 = 1.13 X107 cm/s, and X2/XI = 2.13, one can get TI/T2 = 1.03 with the help of equation (4), which

indicates that X-ray emission times in the absence and presence of magnetic field are nearlysame, which is in good agreement with the streak camera measurement as T} -T 2 -1.5 ns (withZapon filter). This simple analysis confirms nearly two times enhancement in X-ray emissionin the presence of magnetic field as a result of increase in plasma density, which is in closeagreement with the experimental observation. Since increase in density as a result of deceler-ation occurs in comparatively low-temperature region, so the dominant process there will beradiative recombination. A good agreement between analysis and observation indicates that anincrease in plasma density in the X-ray emitting zone as a result of magnetic confinementseems to be the reason behind enhancement in X-ray emission in the presence of magneticfield.

S. ConclusionIn summary, we can say that X-ray emission increased by 2-3 times when laser produced

plasma was expanding across uniform magnetic field of 0.6 T. Enhancement in X-ray emissionis found to be dependent on intensity of external magnetic field and is correlated with anincrease in confinement of laser produced plasma as well as generation of instabilities in theplasma. A simple analysis shows that X-ray emission is inversely proportional to the cube ofX-ray emitting plasma size or the product of expansion velocity and emission time. This modelexplains our experimental observations qualitatively. However there is a possibility of im-provement in the model by including the other plasma parameters. Enhancement in X-rayemission seems to be due to increase in the plasma density in comparatively low-temperaturezone as a result of plasma confinement where probability of radiative recombination goes up.Even enhancement in X-ray emission at high chamber pressure in the absence of magnetic fieldalso seems to be due to dominance of radiative recombination as a result of decrease in plasmatemperature and increase in plasma density in the presence of high neutral density of gasmolecules in the chamber. However the presence of magnetic field at high chamber pressure

.E

Laser produced plasma in magnetic field 443

enhances collisional cooling of plasma or absorption of X-ray emission in background. An-

other observation in this experiment was the generation of high energy ions having expansion

velocity -108 cm/s in the presence of magnetic field, which will be reported separately. It was

also noticed that generation of instabilities takes over after a certain threshold of laser intensity,

which is also a function of intensity of magnetic field. This threshold laser intensity goes down

with an increase in magnetic field.

Important findings of this experiment were that the magnetic confinement of laser produced

plasma generates many effects out of which enhancement in X -ray emission may be applicable

in many other ways.

AcknowledgmentsThe authors are grateful to D.O. Bhawalkar for helpful suggestions and interest during

this work. R.S. Shinde is gratefully acknowledged for providing ferrite magnets for this

experiment.

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