Laser interaction based on resonance saturation (LIBORS):
`an alternative to inverse bremsstrahlung for coupling
`laser energy into a plasma
`
`R. M. Measures, N. Drewell, and P. Cardinal
`
`Resonance saturation represents an efficient and rapid method of coupling laser energy into a gaseous medi-
`um.
`In the case of a plasma superelastic collision quenching of the laser maintained resonance state popula-
`tion effectively converts the laser beam energy into translational energy of the free electrons. Subsequently,
`ionization of the laser pumped species rapidly ensues as a result of both the elevated electron temperature
`and the effective reduction of the ionization energy for those atoms maintained in the resonance state by the
`laser radiation. This method of coupling laser energy into a plasma has several advantages over inverse
`bremsstrahlung and could therefore be applicable to several areas of current interest including plasma chan-
`nel formation for transportation of electron and ion beams, x—ray laser development, laser fusion, negative
`ion beam production, and the conversion of laser energy to electricity.
`
`Introduction
`
`In many diverse applications lasers are used to heat
`and ionize a medium.
`In the ‘plasma field the most
`well-known examples are:
`laser fusion; x—ray laser de-
`velopment; and laser heating of magnetically confined
`plasmas. There is also some interest in the possibility
`of converting laser energy into electrical energy for space
`probes via a thermoelectric process} In almost all cases
`inverse bremsstrahlung plays the important role of
`converting laser energy into plasma energy.
`The purpose of this paper is to show that laser satu-
`ration of an atomic resonance transition of some major
`constituent of a gaseous medium represents an attrac-
`tive alternative mechanism for coupling laser energy
`into the medium, whether it be a plasma or cold and
`un-ionized. Measures? was the first to suggest that this
`approach could be used to enhance substantially the
`ionization of a plasma. According to Measures? laser
`resonance saturation leads to both a heating of the
`electrons via superelastic collision quenching of the
`overpopulated resonance level and an effective reduc-
`tion of the ionization energy of such laser excited atoms
`
`When this work was done all authors were with University of To-
`ronto, Institute for Aerospace Studies, Downsview, Ontario M3H 5T6.
`N. Drewell is now at Atomic Energy of Canada, Chalk River, On-
`tario.
`Received 16 August 1978.
`0003-6935/79/ll1824-04$00.50/0.
`© 1979 Optical Society of America.
`
`1824
`
`APPLIED OPTICS / Vol. 18, No. 11 / 1 June 1979
`
`by the photon energy. These two effects lead to a very
`rapid and almost complete ionization of the medium,
`once the electron density exceeds some threshold value.
`Just prior to ionization burnout, however, there is a very
`rapid rate of laser energy deposition into the plasma.
`If the medium is cold initially, there are several
`mechanisms for generating the seed electrons.
`If the
`laser irradiance is high (several orders of magnitude
`greater than needed to saturate the transition), multi-
`photon ionization from the resonance level is likely to
`predominate in creating these initial free electrons.“
`On the other hand, for more modest values of the laser
`irradiance, associative ionization can (for many atoms)
`lead to the formation of such free electrons.5
`In principle, this approach can be used with all ele-
`ments.
`In reality, however, current laser technology
`imposes some restriction on the range of elements that
`are actually amenable to this laser ionization based on I
`resonance saturation (LIBORS) technique. The larger
`the energy gap being pumped the greater is the energy
`fed directly into the free electrons via superelastic col-
`lisions. Consequently, multiphoton saturation may be
`worth considering in certain instances.
`We have shown elsewhere3 that LIBORS appears to
`be particularly well suited for creating long plasma
`channels that will be needed for electron (or ion) beam
`transportation in certain future inertial fusion schemes.
`We have estimated that plasma channels of 5-m length
`with an electron density of about 1015 cm”3 could be
`created with less than 1 J of laser energy. We also be-
`lieve that LIBORS could be used to create a charge ex-
`change plasma that would be ideal for negative ion beam
`formation.
`
`(cid:34)(cid:52)(cid:46)(cid:45)(cid:1)(cid:18)(cid:17)(cid:20)(cid:22)
`
`ASML 1035
`
`

`

`A;
`
`Ne
`
`KM,
`
`represents the effective resonance
`transition probability, allowing for
`self-absorption,”
`represents the free electron number
`density, and
`for
`represents the rate coefficient
`electron collision induced transitions
`
`between levels oz and B, respectively.
`_
`The ratio of the resonance to the ground state popu-
`lation densities closely approximates the infinite tem-
`perature limit, viz.,
`
`N
`
`2 §2_g
`
`(4)
`
`under conditions of saturation.
`
`The energy equation for the free electrons can be
`divided into two equations, one for the growth of the
`free electron’s mean translational energy 69, viz.,
`d
`Ne if = NeN2K2lE21+ l2E21 " Ec2 " 6elN2tT§2¢)F2
`n=20
`
`+ 2 [E21_ Ecn _ 5eiNnVi11c)F+ QIB
`n3n*
`=20
`+ N2 "2 K... (E... + e.)
`n>1
`n=20
`_Nc Z NnKr1c(Ecn+5e)
`n21
`
`_Ne(-‘ —NoNaHeu _N¢%Hei:
`
`represents the two-photon ionization rate
`coefficient for the resonance level,
`represents the laser photon flux den-
`sity,
`
`where
`
`0%)
`(cm4 sec)
`
`F
`
`(photons
`cm‘?
`sec‘1)
`05,12 (cm2)
`
`Q13
`
`represents the cross section for single
`photon ionization. The sum extends over
`all n 2 n* for which single—phot0n ion-
`ization can be achieved;
`represents the volume heating rate arising
`from inverse bremsstrahlung“;
`for a
`Km represents the rate coefficient
`three-body recombination into level n;
`NeC represents the energy loss of the free .
`electrons arising from the net upward
`movement of bound electrons due to in-
`
`elastic collisions3;
`represents the atom number density;
`Na
`Hm represents the free electron energy loss
`rate coefficient due to elastic collisions
`with atoms; and
`represents the free electron energy loss
`rate coefficient arising from Coulomb
`scattering collisions with ions.”
`The other equation governs the rate of growth of ion-
`ization, viz.,
`'
`
`He,
`
`dN
`I
`
`=
`T
`=
`'’ = Nzaaw + "23" N.o<.12F + N. "§° MK...
`n2n*
`n21
`
`2 n=20
`_ Ne Z [NcKcn +
`I121
`
`(6)
`
`1June 1979 / Vol. 18, No. 11 / APPLIED OPTICS
`
`1825
`
`
`
`NeK23
`
`T3
`
`{RESONANCE LEVEL}
`
`SUPERELASTIC
`COLLISIONS
`
`MULTIPHOTON
`IONIZATION
`
`<réE’F2
`
`SATURATION ls,“
`
`{GROUND LEVEL }
`
`Fig. 1. Simple LIBORS model.
`
`LIBORS Model and Calculations
`
`Considerable physical insight into the various inter-
`actions arising when laser radiation is used to saturate
`a resonance transition can be gained by reference to Fig.
`1. Under high density conditions (i.e., very short de-
`phasing time), a rate equation analysis is applicable.7
`We have formulated a computer code that utilizes a
`20-level model of the laser excited atom and have un-
`dertaken detailed calculations for the case of sodium
`
`vapor.6~8
`Under saturating conditions, Measures9 has shown
`that a population redistribution occurs between the two
`levels in a time
`T
`
`75 E [(1+ 5'2/é.’1)R21l"]»
`
`(1)
`
`where g2 and g1 represent the respective degeneracies
`of the upper and lower levels, and
`
`R21i'='B21 fI’(V)1 21(V)dl'/471'} (S851)
`
`represents the stimulated emission rate
`coefficient for the (2-1)
`resonance
`transition,
`represents the spectral irradiance of
`the radiation field at frequency :2 ap-
`propriate to the resonance transition,
`represents the appropriate Milne
`coefficient, and
`represents the resonance line profile
`function.
`
`I (11)
`
`B21
`
`621(1))
`
`The saturating condition can be expressed in the form:
`I [(12) >> I, (v), where the saturated spectral irradiance,
`
`T§AD
`
`hv
`
`c
`
`150/) E
`
`87rh1/3
`
`(1 + gwl
`
`~r]§AD
`T2
`
`l ’
`
`(2)
`
`represents the radiative lifetime of the
`resonance transition {T§AD = A511},
`represents the laser photon energy {=
`E21, energy difference between levels
`2 and 1},
`is the velocity of light,
`
`-1
`
`T25 [A§1+ Ne {K21 4“ K12 4' 2 Km”
`
`m>2
`
`(3)
`
`represents the effective lifetime of the
`laser pumped level,‘5
`
`

`

`
`
`
`
`POPULATIONDENSITIES(cm-3)
`
`
`
`
`
`ABSORBEDLASERPOWERDENSITY,o¢(wc,,,-s,
`
`
`
`
`
`200
`I00
`’
`O
`TIME from ONSET of LASER RESONANCE SATURATION
`(nsec)
`
`Fig. 2. Temporal variation of electron density Ne, electron tem-
`perature TE, ion temperature T,-, Ng(3p) resonance and N4(3d) ex-
`cited state populations, and absorbed laser power density Q‘ as pre-
`dicted by LIBORS code for sodium with N0 = 1015 (cm'3) and I’ =
`105 (W cm'2).
`
`£
`—: Qmox (LIBORS EON. 9)
`z
`0
`Qrnax (LIBORS cooa)
`——— Q15 INVERSE BREMSSTAHLUNG
`( N3 = No/2 )
`
`
`
`
`
`MAXIMUMLASERPOWERABSORBEDPERUNITVOLUME(Wcm‘3l
`
`
`
`
`
`
`
`INITIAL SODIUM DENSITY. No(C|T1'3)
`
`Fig. 3. Comparison of the variation in maximum laser energy de-
`position rate with initial sodium density as predicted by LIBORS
`code, simple LIBORS model, and for inverse bremsstrahlung (the
`latter for three values of laser irradiance).
`
`1826
`
`APPLIED OPTICS / Vol. 18, No. 11 / 1June 1979
`
`where [5(n) represents the radiative recombination rate
`coefficient into level n.
`
`The solution of Eqs. (5) and (6) in conjunction with
`the appropriate set of 20 population density equationss-8
`yields solutions such as those presented in Fig. 2.
`In
`this instance the initial sodium vapor density was as-
`sumed to be 1015 cm‘3, and the laser irradiance was
`taken to be 1 MW cm”? at 589 nm consistent with the
`
`experiments of Lucatorto and McIlrath.13 Two—photon
`ionization from the resonance level and single—ph0ton
`ionization from n > 3 levels are taken into account.3
`
`The particularly noteworthy features of this inter-
`action are as follows: The electron temperature jumps,
`within a few nanoseconds of the redistribution of the
`population between the resonance and ground levels,
`to‘ a plateau value that is in essence determined by a
`balance between collisional excitation and superelastic
`quenching of the resonance state.” Ionization pro-
`ceeds with a rate that is first determined by two—photon
`ionization of the laser maintained resonance state
`population.
`(For lower laser power densities associative
`ionization might be significant.) Once the free electron
`density exceeds 1012 cm“3, electron collisional ionization
`of the resonance level and single-photon ionization of
`the higher levels appear to take over and further ac-
`celerate the rate of ionization. During the final ion-
`ization burnout phase a momentary drop of the electron
`temperature is seen to be predicted.
`Under saturating conditions, the attenuation of the
`laser beam can be expressed in the form-9-~5
`
`d1‘(2)/dz = -62’
`
`(W cm‘3),
`
`(7)
`
`where Q’ represents the net volume rate of power dis-
`sipation for the laser radiation and comprises the laser
`power dissipated in maintaining the resonance state
`population against (1) superelastic quenching [the first
`term on the right-hand side of Eq. (5) and represents the
`primary electron heating mechanism], (2) excitation to
`higher levels, and (3) spontaneous emission. The
`temporal variation of Q’, at a sodium density of 1015
`cm“3, is shown in Fig. 2. Evidently, Q’ increases rapidly
`with increasing electron density reaching a peak just
`prior to ionization burnout. Our computer calculations
`clearly indicate that the superelastic heating term‘
`
`QSE 7* NcN2K21E21
`
`(8)
`
`dominates Q’ at this time (i.e., N2 ~ Ne w N0/2) in
`which case the relation
`
`I... = GN3K21E21/4
`
`(9)
`
`is closely approximated over several orders of magni-
`tude variation in N0, as seen by reference to Fig. 3 where
`G E (g2/g1)/(1 + gg/g1), and No represents the original
`sodium atom density prior to laser irradiation.
`fnax thus expresses the maximum rate of laser energy
`deposition into the plasma, and as such we wish to
`compare it with the rate of laser energy deposition Via
`inverse bremsstrahlung,“ viz.,
`
`1.17 x 10-7N3 A21’
`12c2(;eT,,)8/2
`
`Q” =
`
`(10)
`
`

`

`where we have assumed N9 = NU/2 in order to make a
`comparison with Qf,,,,,,, >\(cm) represents the laser
`wavelength, Te represents the electron temperature
`(with kTe in eV), and I 1 (W cm‘2) is the laser irradiance.
`A direct comparison of the rate of laser energy deposi-
`tion through LIBORS and inverse bremsstrahlung can
`be obtained from the ratio of Eqs. (9) and (10), viz.,
`
`.
`
`(1.,
`
`_
`
`-
`
`1.17 x 10‘7N§>\2I’
`‘
`Que
`The maximum value of laser irradiance needed in the
`LIBORS case to produce a deposition rate of Qfm, over
`a plasma depth L is, from Eq. (7), simply Qfinax L. We
`can, for a given situation, deduce the minimum value
`of H (that is, the most conservative ratio) by setting
`
`1’ =
`
`("ML
`
`in Eq. (11). Clearly, if we express
`
`Q13 = I1/LIB:
`
`(12)
`
`(13)
`
`L13 represents the characteristic absorption length for
`inverse bremsstrahlung.
`In which case we can write
`
`12c2(IeT,)-W
`L“,
`(14)
`Hm“ _ L -1.17 x 10‘7N§>\3L '
`Hmin represents the minimum value for the rate of
`laser energy deposition via LIBORS along the path of
`the laser beam compared with inverse bremsstrahlung
`and is equal to the ratio given by Eq. (11) at the point
`of entry of the laser beam into the plasma. As the laser
`beam penetrates the plasma and is attenuated, the de-
`gree of coupling to the plasma via LIBORS is undi-
`minished, but that through inverse bremsstrahlung
`decreases with I 1. Thus H increases with penetration
`through the plasma. Nevertheless, Hmin is a useful
`quantity since it provides us with a conservative value
`for
`the
`advantage
`of LIBORS over
`inverse
`bremsstrahlung for a given situation, independent of
`the detail characteristics (such as G and K21) of the
`particular atom being pumped.
`It should be noted that
`if excess laser power is available, such that I1 >> Qf,,,,,,L,
`Eq. (11) has to be used, and Hmin is no longer mean-
`ingful.
`Indeed as seen in Fig. 3, for very high values of
`[[1 QIB > Qinaiv
`-
`In the case of alkali metals, the laser wavelength will
`lie in the visible to near IR, and the appropriate value
`of kTe will be around 1 eV.
`Indeed, for sodium, A = 589
`X 10”7 cm, and we may set kTe = 1 eV. Under these
`circumstances,
`
`Hmin * (2-66 X 1037)/(N§L),
`
`.
`
`(15)
`
`and we can see that for typical plasmas (L = 1 cm), Hmin
`can range from 2.66 X 109 at N0 = 1014 cm”3 to 2.66 X
`103 at N0 = 1017 cm'3.
`
`Discussion and Conclusions
`
`It is thus quite evident that LIBORS represents a
`mode of coupling laser energy into a plasma that can be
`many orders of magnitude greater than achieved
`through inverse bremsstrahlung for the same laser
`power. Put another way, LIBORS requires a much
`
`lower laser irradiance to accomplish the same rate of
`laser energy deposition into the plasma, or the effective
`absorption length for LIBORS is very much less than
`that for inverse bremsstrahlung. An additional at-
`tractive feature of the LIBORS approach is that it can
`be used in cases of a cold (i.e., un-ionized) gaseous me-
`dium.
`«
`
`It is also worth noting that if a laser is tuned to satu-
`rate a resonance transition of the singly charged ion, the
`superelastic heating term
`
`Q” = N.Né’K§’.E§’.
`
`(16)
`
`would be very large over the entire period to second
`stage ionization burnout, and not have just a sharp peak I
`as indicated in the case of first stage ionization burnout.
`N (11, K and E refer to the singly charged ion values
`of resonance state population density, superelastic
`collision rate coefficient, and resonance to ground en-
`ergy separation.
`Strontium represents an interesting candidate since
`resonance lines in both S,I and SrII (460.7 nm and 421.6
`nm, respectively) could be pumped simultaneously by
`a dual wavelength flashlamp pumped dye laser. As
`shorter wavelength lasers become available, higher
`stages of ionization would become accessible to this
`LIBORS approach.
`In summary the advantages of LIBORS over inverse
`bremsstrahlung as a means of coupling laser energy into
`a gaseous medium are:
`(1) much higher rate of energy deposition;
`(2) more efficient interaction;
`(3) operates at much lower laser power levels;
`(4) much shorter interaction length;
`(5) laser beam attenuated linearly as energy deposi-
`tion is uniform along the beam;
`(6) cold start capability even at modest laser power
`levels.
`It should also be noted that LIBORS can lead to al-
`most complete ionization very much faster than the
`corresponding multiphoton rate. Of course all the
`above discussion relates to reasonably high density (No
`> 1013) situations.
`
`This work was supported by USAF/AFOSR under
`grant 76—2902B and the National Research Council of
`Canada.
`
`References
`1. K. W. Billman, Astronaut. Aeronaut., 56 (July 1975); L. K. Hansen and N. S. Rasor,
`“Thermo Electronic Laser Energy Conversion", 2nd NASA Laser Energy Conversion
`Conference, NASA~Ames, January 1975, NASA SP-395.
`2. R. M. Measures, J. Quant. Spectrosc. Radiat. Transfer 10, 107 (1970).
`3. R. M. Measures, J. Appl. Phys. 48, 2673 (1977).
`4. R. M. Measures, N. Drewell, and P. Cardinal, “Superelastic Laser Energy Conversion
`(SEI.EC)”, Prog. Astronaut. Aeronaut. G1, 450 (1978).
`5. A. V. Hellfeld, J. Caddick, and J. Weincr, Phys. Rev. Lett. 40, 1369 (1978).
`(g, R. M. Measures, N. Drewell, and P. Cardinal, "Electron and Ion Beam Transportation
`Channel Formation by Laser Ionization Based on Resonance Saturation—LIBORS“,
`J. Appl. Phys. (April 1979].
`7. T. J. Mcllrath and J. L. Carlsten, Phys. Rev A 6. 1091 (1972).
`8. R. M. Measures, N. Drewell, and P. Cardinal, “Rapid and Efficient Laser Ionization
`Based on Resonance Saturation" (in preparation).
`9. R. M. Measures, J. Appl, Phys. 39, 5232 (1968).
`10. T. Holstein, Phys. Rev. 83, 1159 (1951).
`J. M. Dawson, Phys. Fluids 7. 981 (1964).
`,
`E. J. Morgan and R. D. Morrison, Phys. Fluids 8, 1608 (1965).
`13. T. B. Lucatorto and T. J. Mcllrath, Phys. Rev. Lett. 37, 428 (1976); T. J. Mcllrath and
`T. B. Lucatorto, Phys. Rev. Lett. 38, 1390 (1977).
`
`1 June 1979 / Vol. 18, No. 11 / APPLIED OPTICS
`
`1827
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`