RAPID COMMUNICA TIONS

This section was established to reduce the lead time for the publication of Letters containing new, significant material in rapidly advancing areas of optics judged compelling in their time­liness. The author of such a Letter should have his manuscript reviewed by an OSA Fellow who has similar technical interests and is not a member of the author's institution. The Letter should then be submitted to the Editor, ac-conipanied by a letter of endorsement from the

Cautionary Note Concerning the CUSO4 X-Ray Laser

Kenneth W. Billman and Hans Mark

NASA Ames Research Center, Moffett Field, California 94035. Received 6 August 1973. Sponsored by Sumner P. Davis, University of California at Berkeley. Recently, Kepros et al. have reported1 x-ray laser action

obtained by focusing the 1.06-µm radiation of a Q-switched Nd 3 + glass laser to a small cylindrical volume inside a CuSO4-doped gelatin medium supported between two glass plates. Several attempts to confirm their obser­vations have been made by a Naval Research Laboratory group,2,3 Boster,4 and in this laboratory. The results so far have been inconclusive. Elton et al.2 have observed spots on films similar to those reported by Kepros et al.,1

but they have not been able to observe collimated x-ray beams using electronic detectors.3 Experiments peг-forrtied at this laboratory with electronic detectors have also failed to show collimated x rays. Boster4 has sug­gested an alternate mechanism for producing spots on the film that depends on static electric discharges. However, his proposal does not account for the fact that both groups have found the spots to be localized on the film, all falling within a 1-cm circle whose center is approximately at the intersection of an extension of the axis of the plasma re­gion, produced in the medium by the pump laser, and the film surface. (The Elton group observed as much as 2.2-cm displacement of the circle center at higher laser ener­gies.) Since the electrostatic discharge spots would occur randomly throughout the 12.7-cm X 17.8-cm film used, it would appear that such discharges cannot be responsible for the observations of the two groups.

No mechanism for the x-ray lasing action that was claimed by Kepros et al. has been proposed. It is the purpose of the present note to suggest an alternate expla­nation of the collimated x-ray beams that might be creat­ed under the conditions described in the experiment of

OSA Fellow (who in effect has served as the referee and whose sponsorship will be so in­dicated in the published Letter) and a commit­ment from the author's institution to pay the publication charges. The Letter will be pub­lished without further refereeing. The latest Directory of OSA Members, including Fellows, was published as Part 2 of the August 1969 issue of the Journal of the Optical Society of America.

Fig. 1. Geometry of the x-ray experiment model. The high tem­perature plasma cylinder, of radius a and length /, is embedded in the low temperature, oxygen-rich absorbing medium with the output window lying in the 2 = 0 plane. A photon, originating from the unobscured area Aθ, z), emitted at angle θ relative to the cylinder axis, passes through this window and, if not absorbed in air, reaches the film plane at position r = L tanθ. For clarity, the relative dimensions of the figure have been highly distorted;

actually, L » l » a.

November1973 / Vol. 12, No. 11 / APPLIED OPTICS 2529

Kepros et al., which does not depend on the assumption of laser action in copper.

Numerous experiments5 have demonstrated the ability of high intensity Nd3+ glass laser pulses to internally heat solids to high energy density, radiative plasmas. In some cases, substantial conversion to x-ray radiation has been observed.6 This is especially true if the pump pulse con­tains picosecond substructure such as Kepros occasionally observed.7 (It should be noted that the experiments re­ported by Elton et al.2 were also performed with a laser that exhibited occasional mode-locking.8 Improvements to the system have eliminated this. New experiments re­ported in Bradford et al.3 should be viewed mindful of this possibly essential difference.) We assume here that such heating resulted in sufficiently high energy densities to produce K-shell ionization in copper and subsequent emission of copper K fluorescence x rays in the above-mentioned experiments. An examination of the absorp­tion of this plasma emission in the surrounding media of these experiments shows that it is dominated by water (the linear absorption coefficient ~9.91 c m - 1 ) . This phenomenon primarily results from the photoionization of oxygen (the K edge is at 23.3 A or 532 eV). This strong ab­sorption would prevent the escape of K x rays in all direc­tions. In the plasma, however, where most of the elec­trons have been removed from the oxygen atoms (very likely a region that is smaller than the focal volume), ab­sorption would be negligible. In effect, the laser pulse produces a narrow low absorption channel for the trans­mission of the copper fluorescence x rays. Because the line focus of the laser beam was extended beyond the edge of the medium in these experiments, the end face of this plasma cylinder was not bounded by high absorption ma­terial, and therefore it provided the exit window through which the x rays could escape and proceed with moderate air attenuation (µ ~0.005 c m - 1 ) to the recording film.

In order to predict the x-ray flux at the film surface, we consider a simple model in which the plasma is contained in a cylinder of radius a and length l (with l » a), as shown in Fig. 1; it is filled with n copper ions per unit vol­ume, radiating isotropically with a spontaneous decay rate of R photons/sec. Because of absorption, we only consid­er those photons that have an emission direction passing through the z = 0 (output) face. The emission rate from the volume element πa2 dz into a solid angle dΩ at angle θ is

The quantity A(θ,z) is the unobscured area

where u = z tanθ/2a. We wish to calculate F(θ), the number of photons arriving at the film surface per unit area, for a successful shot, that is, one for which film ex­posure would be obtained. Assuming that such a shot produces a stable, high energy density plasma cylinder for

Table I. Peak Photon Density at the Film

Fig. 2. Variation of x-ray photon density at the film plane as a function of θ. The plots are normalized to the peak density at θ

= 0.

a lifetime T, noting that the solid angle subtended by the film area element da is dΩ = cos3θ dσ/L2, and including the air attenuation by a transmission factor ~exp ( -µL) , we find from Eqs. (1) and (2) that

The peak value, which occurs for θ = 0, can be shown to be

and the angle for which Fθ) decreases to F(0)/2 is θ1/2 = 5a/3l.

In the CuSo 4 experiments, l ~ 1 cm and 30 cm ≤ L ≤ 110 cm. A reasonable spontaneous emission rate for the copper K transitions9 is R = 1015 s ec - 1 . The upper limit of the plasma lifetime would be the laser pulse length of 20 nsec; however, hydrodynamic considerations probably set a limit of T ~ 1 nsec. We will assume T = 0.1 nsec. For a 1 0 - 3 mole CuSO4 solution, the number density of copper atoms is 6 X lO17 c m - 3 . It is clear that the num­ber density of ions capable of emitting K fluorescence must be less than this atom density; we will assume n = 1 0 - 6 (6 X 1017 c m - 3 ) = 6 X 1011 c m - 3 . In Fig. 2 are shown typical plots of the photon density, normalized to peak value at 0 = 0. The values of F(0) are given in Table I.

2530 APPLIEDOPTICS / Vol. 12, No. 11 / November 1973

To assess the spot size that would result from these photon densities and would be photographically recorded on the Kodak No-Screen medical film used, we note that for 8-keV x rays, a film density of 1 requires F1 ~ 4 X 107

photons/cm2 and a threshold density of 0.1 requires FT ~ 3 X 106 photons/cm2. From Table I and Fig. 2, one finds that for the a = 5 µm curve and L = 30 cm, Fθ) drops to FT at a radius of 0.009 cm. This value agrees well with the spot diameter of 0.02 cm observed by Kepros et al. Furthermore, from a numerical integration, one finds that the total number of photons that escape through the end face of the 5-µm filament is 6.8 X 106. This number also agrees well with an electrometer measurement7 by Kepros of lO4-l05 photons, if the solid angle subtended by the instrument is taken into account. Thus, we can con­clude that a small diameter, high energy density plasma filament similar to those observed in laser gas break­down,10 with reasonable parameter assumptions, leads to a correct spot size and total photon number for the film I)osition L = 30 cm.

However, because of beam spread and air attenuation, the peak photon density for this 5-µm filament with L = 110 cm is less than 3 X 106 photons/cm2, so that even for a very small diameter, a spot probably would not be seen above film background. The solution to this dilemma is very likely one of a number of possibilities that can only be mentioned in this brief note. First, the possibility ex­ists that a spot (perhaps of smaller radius than 0.009 cm) could be observed at a density less than 0.1. This possi­bility demonstrates the necessity of using a densitometer scan or other more quantitative means to assess accurate­ly the spot size. Second, an examination of the refractive index differences in the various media of the sample indi­cate that some total x-ray reflection could result in higher peak flux. Third, our uniform plasma cylinder model is too simple; the Gaussian intensity distribution in the laser beam would probably produce an ellipsoidal high energy density region, which again would lead to x-ray flux dis­tributions that are more highly peaked than those of Fig. 2. Finally, the latter type of energy distribution in the plasma would also lead to a decrease of x-ray refractive index with plasma radius, thus effectively producing a positive lens to collimate the fluorescence x rays.

We believe that the assumptions made in the calcula­tions presented in the preceding paragraphs are reason­able and that the mechanism proposed is quantitatively consistent with the observations reported by Kepros et al. In the absence of a laser mechanism that could explain laser action in the copper K x-ray region, we believe that the explanation given here of the collimation effect is, most likely, the correct description of the phenomenon that may have been observed.

The authors would like to express their appreciation to Paul Rowley and James Stallcop for helpful discussions during the course of this calculation.

References 1. J. G. Kepros, E. M. Eyring, and F. W. Cagle, Jr., Proc. Nat.

Acad. Sci. (U. S.) 69, 1744 (1972). 2. R. C. Elton, L. J. Palumbo, R. A. Andrews, R. C. Eckardt,

and J. N. Bradford, Appl. Opt. 12, 155 (1973). 3. J. N. Bradford, R. C. Elton, T. N. Lee, R. A. Andrews, L. J.

Palumbo, and R. C. Eckardt, Appl. Opt. 12, 1095 (1973). 4. T. A. Boster, Appl. Opt. 12, 433 (1973). 5. For example, see Sec. VI in Laser Interaction and Related

Plasma Phenomena, H. J. Schwarz and H. Hora, Eds. (Ple­num, New York, 1972), Vol. 2, p. 389.

November1973 / Vol. 12, No. 11 / APPLIED OPTICS 2531

6. P. J. Mallozzi, Paper D.7, 7th International Quantum Elec­tronics Conference, Montreal, Canada, 8-11 May 1972.

7. J. G. Kepros, Utah U., private communication. 8. R. A. Andrews, Naval Research Laboratory, private communi­

cation. 9. M. A. Duguay and P. M. Rentzepis, Appl. Phys. Lett. 10, 350

(1967). 10. A. J. Alcock, in Laser Interaction and Related Plasma Phe­

nomena, H. J. Schwarz and H. Hora, Eds. (Plenum, New York, 1972), Vol. 2, p. 155.