Pulsed X-Ray Laser Amplifier

Recent advances in the semiconductor processing industry and in x-ray crystallography for biochemical and medical applications have demonstrated the need for more intense, coherent beams of shorter wavelengths or higher brightness, than currently achievable with the newly developed far UV lasers and expensive synchrotron laser sources. Current femtosecond-regime laser-produced plasmas offer the potential of high brightness x-ray sources, but to date suffer from lower than needed photon fluxes due to large bandwidths and relatively large angular divergences in the x-ray beams produced. While there is currently work in progress to overcome these limitations (e.g., the recent patent application referenced above by this inventor), these efforts may be of more value as drivers for dense plasma recombination x-ray lasers than as direct producers of non-coherent x-rays. Other, earlier techniques are briefly described in the following paragraphs.

Free-electron lasers, for example, are candidates for UV and x-ray generation and are presently under development. However, these devices will require very high energy electron beams to reach these wavelengths. In addition to the high cost, technical complexity, and size of these electron beam sources, the gain of FEL devices will be small at these frequencies since the gain scales as 1/.gamma..sup.3, where .gamma./2 is the electron beam energy. It may not be possible to sustain laser oscillations if the gain is comparable to system losses. At present, no high power FEL's exist at sub-visible wavelengths.

Excimer lasers are another technology being developed for output in the UV regime. These devices are at present limited to significant gains in the region above about 2,000 Angstroms. They also require expensive and large electron beam systems for excitation, are limited to pulsed operation, and use highly toxic and corrosive gases.

Plasma lasers have recently been investigated and predictions of potential high energy operation have been made. At present, two techniques have been utilized to generate population inversions; high and low voltage plasma arcs and laser initiated plasmas. Both are limited in the volume of plasma produced and thus the present invention represents a significant improvement in the state-of-the-art of plasma lasers in several important aspects.

The advent of femtosecond-regime pulsed lasers, enabled by use of chirped pulse amplification (CPA) techniques, has allowed the production of high energy electrons (as described in U.S. Pat. No. 4,570,103), via ponderomotive and plasma acceleration processes, which can be used in a variety of techniques (reference application Ser. No. 09/135,164) to produce x-rays. One embodiment of this invention makes use of these short-pulse lasers to produce a plasma tube, of the order of several centimeters or less which contains fully ionized plasma(s) of high Z atoms and energetic electrons, which serve as the medium for build-up of population inversions on low level atomic states (e.g., n=3 to 2 transitions) by recombination processes. The plasma tubes, of the order of several microns in diameter, are produced over lengths of several centimeters by extension of the Rayleigh range by a combination of plasma self-focusing and plasma refractive index "shaping" using the laser beam radial profile, or by auxilliary lasers to pre-condition the plasma (reference C. G. Durfee III and H. M. Milchberg, Physical Review Letters, Vol. 71, No. 15, Oct. 11, 1993, pg. 2409). Because the plasma is created on time scales of the order of femtoseconds, and the recombination cascade, even at high plasma densities, is relatively slow, the presence of high energy electrons cannot initially de-populate the inversion on lower levels, because they have not yet been created by radiative or three-body recombination processes. At time scales of the order of nanoseconds or less, the necessary population inversion builds up. However, the remaining electron plasma cannot significantly de-populate these inversions, either because the electron temperature is too high (and therefore preferentially depopulates states at or below the bottom level of the inverted state population (e.g., n=3), or due to subsequent laser and/or electron beam pulses which condition the electron temperature so as to minimize de-population of the inversion.

At the time of maximum population inversion, a "seed" x-ray pulse is injected into the plasma column, and is amplified by the stimulated emission process. This seed x-ray pulse can be generated by similar short-pulse x-ray techiques previously referenced, and be conditioned to have low angular divergence by use of x-ray capillary collimation techniques. This will insure that the main x-ray output pulse will build up from seed photons that are preferentially oriented, and will increase the number of output x-ray photons within milli-radian angular limits.

The microwave-driven plasma laser described herein achieves the required population inversion by direct control of the plasma electron temperature through the use of electron cyclotron resonance heating (ECRH). This allows the control of the fractional ionization and electron temperatures at various times in the laser process which provides a valuable parameter with which to optimize the performance of plasma lasers. In addition, the use of ECRH allows the production of sufficiently dense plasmas in a controlled fashion with large volumes feasible for high power output. The lasing volume is limited only by the ability of the microwaves to penetrate the plasma and the self absorption of the laser radiation by the plasma. These restrictions can be somewhat reduced by making the plasma optically thin in one dimension for both laser and microwave radiation.

In the preferred embodiment of the invention, microwaves enter the plasma, which is located in a magnetic field of value such that electrons in the plasma undergo cyclotron motion under the influence of the electric field of the microwave radiation and thus gain energy, raising the electron temperature. Rapid heating by microwaves causes the plasma to become highly ionized, creating population inversions which result in laser transitions in the UV and x-ray regions of the spectrum. The microwave power is then adjusted to minimize collisional de-excitation of the upper laser levels, along with radiational cooling and expansion cooling, to allow maximum laser output.

The initial plasma generation can be accomplished with the same microwave-frequency as used to control the lasing process. For ion species of solid elements, a separate ECRH system may be necessary to create the desired plasma via a sputtering process. In both cases, large volumes of plasma can be generated, as opposed to the limited diameter plasma column generated in present arc-driven plasma lasers (W. T. Silfvast, O. R. Wood, and J. J. Macklin, Applied Physics Letters, Volume 42, Page 347 (1983)).

The use of ECRH allows very efficient couplings of energy into the plasma, allowing modest power requirements for the microwave source. In addition, the use of microwaves allows control of the electron temperature, a feature lacking in the arc-driven laser process. Although auxilliary lasers can also heat the plasma electrons, very high powers are required to initiate plasma formation. Thus, the plasma lasing region is limited to the focal region for CO.sub.2 driven plasma lasers, which must be small for modest size lasers used for plasma formation.

The use of microwaves for plasma formation and control allows a simple cylindrical configuration for the laser resonator in the UV range of frequencies, since the microwaves can be coupled in a variety of ways to the plasma region. The solenoidal magnetic field used for ECRH will also confine the plasma in the radial direction within the cavity field envelope. Output power from this microwave plasma laser is larger than for other devices previously described due to the potential for large volume and the control of the electron temperature, which directly affects the collisional de-excitation process that limits the magnitude of the population inversion. The simplicity of the excitation process and configuration should allow significant technical and economic performance improvements over prior laser art.

FIG. 1 is a schematic of a pulsed x-ray plasma laser amplifier, including the x-ray "seed" laser and associated equipment.

FIG. 2 is a graph of the population inversion as a function of time, as calculated for a low density plasma (of the order of 1E+15 per cubic centimeter); at higher plasma densities, the population inversion is established at an earlier time.

FIG. 3 is a graph showing the plasma electron temperature for various values of microwave power input for three different neutral density levels;

FIG. 4 is a graph showing plasma electron density for various values of microwave input power for three different neutral density levels;

FIG. 5 is a cylindrical microwave plasma laser with a gaseous source constructed in accordance with the present invention;

FIG. 6 is a rectangular microwave plasma laser constructed in accordance with the present invention;

FIG. 7 is a rectangular microwave plasma laser with a sputtered ion source and slotted waveguide microwave feed constructed in accordance with the present invention;

FIG. 8 is a cylindrical microwave plasma laser utilizing a sputtered ion source and a resonant microwave cavity for pumping the ion population levels which is configured in accordance with the present invention.

FIG. 9 shows a configuration for injecting cool electrons into a femtoseconds laser produced plasma channel, and a microwave produced plasma cylinder.

The following material contains detailed descriptions and the projected performance parameters of the short-pulse laser that produces the plasma needed for x-ray lasing. A schematic is shown in FIG. 1. A source laser 10 provides and initial laser pulse 12 (e. g., a flash lamp-pumped Ti-saphire laser, or a NdYAG glass laser with mode locking and output at 1.06 microns wavelength and several tens of Joules of energy per pulse which can pump a Ti-shaphire after frequency doubling). The output pulse enters the chirped pulse amplifier (CPA) which consists of optical gratings 14 to spatially separate out the pulse Fourier components, a pulse stretching cavity 16, with an embedded mask 18 to modify the phase/amplitude of the now spatially separated pulse Fourier components, and alignment mirror 20 to steer the laser pulses into a laser amplifier 22 and pulse re-compressor 24. The CPA produces a greatly shortened laser pulse 26 of duration several hundred femtoseconds (10.sup.-15 sec) at a preselected location downstream. Laser optics 28 (optional location) produce a diffraction limited focal spot, typically of the order of a few microns or more in diameter. A gas jet 30 provides maximum density gats at the location of the laser beam focal plane 32 which serves as the plasma source. The laser beam, typically with intensities of 10.sup.18 -10.sup.21 W/cm.sup.2 at the focal plane, ionizes the gas creating a plasma source.

The "seed" laser 34 can be a replica of the the system shown in FIG. 1, with x-ray capillary optics 36 to produce a collimated x-ray beam with angular spreads of the order of milli-radians, and a Bragg crystal monochrometer to select the line radiation matching that of the plasma x-ray source desired.

The estimated performance of this laser pumped short-pulse x-ray plasma laser has been estimated based on the following simplified equations describing the physical processes leading to population inversions in the plasma. Although these calculations were made for low density plasmas typical of microwave produced plasmas, similar calculations with higher density plasmas capable of being produced by short-pulse lasers will provide similar results, although the gains will be higher and the timeframes for initiation of lasing will be much shorter.

The following description covers the production of the source plasma by microwave excitation techniques.

The unique and special properties germane to this invention can be best described by considering the various physical processes that take place to produce laser action. The major effects that must occur include ionization, recombination, control of collisional de-excitation, and finally, lasing.

The initial phase of operation of the microwave plasma laser involves the creation of an ionized medium or plasma. To achieve optimum operating efficiency, it is desirable to utilize an energy-efficient ionization process which is capable of producing large volume plasma regions with the appropriate mix of ionization states. Previous plasma laser technology has utilized high and low voltage arcs and high power CO.sub.2 lasers to create an ionized region.

Arc discharges are limited in that the temperatures they attain are limited in the duration of time that the higher temperatures can be maintained. For example, for low voltage arcs, the creation of a plasma column quickly lowers the arc impedance, thus reducing the electric fields and limiting the transfer of energy to the plasma. Thus, although high temperatures may be produced, there is a rapid decay to values in the range of 2000.degree.-4000.degree. K. High voltage discharges may produce higher initial temperatures, but decay is rapid, and in both cases, the plasma volume, is limited to the size of the discharge column. Glow discharges can produce larger volumes but have much lower densities to maintain high impedances.

The use of high power CO.sub.2 lasers to produce a suitable plasma can result in high ionization states and high temperatures. However, this technique at present is limited to small volumes, since the laser beam must be focused to achieve the high power densities required to produce ionization.

In contrast to prior art, this invention utilizes electron cyclotron resonance to create the necessary ionization. It is well known that an electron in a magnetic field B will oscillate at a frequency ##EQU1## If microwave radiation at a frequency .omega..sub.c is introduced, energy is transferred to the electron in resonant fashion, raising its velocity and thus the plasma electron temperature T.sub.e. This mechanism is very efficient at coupling energy into the plasma, as opposed to non-resonant breakdown (i.e. lasers) where very high electric fields are necessary so that the electron reaches ionization energy before elastic collisions reduce its energy.

One of the key parameters in determining the plasma laser output power is the electron density, since this quantity affects the collisional de-excitation rate, which reduces the population inversion required for lasing. An estimate of the electron density and temperature can be obtained from a plasma model recently developed (P. J. Moffa, T. Tajima, and J. J. Thomson, Bulletin of the American Physical Society, Volume 25, Page 958, (1980)) for a cylindrical geometry, as given below: ##EQU2## Typical levels of electron temperature are shown in FIG. 1 and electron density in FIG. 2, for various microwave input powers and neutral density values.

It has been shown (O. R. Wood and W. T. Silfvast, Applied Physics Letters, Volume 41, Page 121 (1982)) that the limiting electron density for lasing is approximately ##EQU3## Note that with microwave excitation, electron temperatures can be made higher than levels in low voltage arc lasers, and can be controlled with input power. Thus the limiting electron density can be higher, leading to higher laser output power. This is a significant feature of the microwave plasma laser which is not found in prior art.

Consideration of the penetration of microwave radiation into the plasma is necessary in designing a practical device. The plasma frequency W.sub.p, where ##EQU4## determines the approximate cut-off frequency for penetration. At high electron densities the plasma must be kept thin so that the microwaves can reach the entire volume for CW operation. For outputs in the near-visible UV region, plasma densities below 10.sup.14 /cm.sup.3 will probably be necessary.

An estimate of the output of a microwave plasma laser can be made by assuming that all electrons produced in the ionization process produce a lasing photon. Using a plasma electron density of 10.sup.14 /cm.sup.3 and assuming a wavelength of about 0.25 microns, one finds ##EQU5## According to FIG. 2, about 60 Kw of microwave power would be required to produce an electron density of 10.sup.14 /cm.sup.3 for the geometry used in the calculations. This configuration has a volume of about 1.5.times.10.sup.4 cm.sup.3 and thus total energy output could be a maximum of 1.25 J per pulse. Plasma recombination in the absence of microwave power is typically of the order of 10.sup.-5 -10.sup.-4 seconds so that repetition rates near 10.sup.3 /sec can be considered possible. This leads to output power of about 1 Kw as compared to about 30 Kw for input power assuming a 50% duty cycle, or an efficiency of about 3%.

The potential for reaching higher ionization states is present for higher microwave powers, since the electron temperature can rise rapidly with increasing power as shown in FIG. 1. Higher levels of ionization leads to shorter wavelength laser transitions and the potential for soft x-ray lasing. The gain per unit length can be expressed as ##EQU6## The population inversion is calculated using ionization rate equations (S. Suckewer and H. Fishman, Journal of Applied Physics, Volume 51, Page 1922 (1980)), and appropriate recombination coefficients. The population inversions are difficult to calculate and experimental verification of the gain values will be necessary to optimize a particular design.

Consider now devices based on the principles of this invention. The physical configuration of a microwave plasma laser will depend to a certain degree on the nature of the lasing ion species. Elements in a gaseous state will have a simpler configuration due to the ease in designing the source. In addition, depending upon the microwave penetration and laser line optical absorption, cylindrical or rectangular geometries can be effective.

Consider now a design for a cylindrical device, as shown in FIG. 3. The source gas enters from the left 21 and enters the resonator region which is located in a solenoidal magnetic field produced by current coils 23. The microwave radiation enters the cavity region via waveguides 25 located along the length of the resonator region. The microwaves only have to penetrate a distance of one radius to fully excite the plasma, and thus the laser can be longer than the skin depth for the microwave radiation. The resonator mirrors are designed to be totally reflecting 27 and partially transmitting 29 to allow laser radiation to build up and exit the cavity. The source gas can be recycled via exit ports 31 which control the neutral density. Depending upon the gain value of the ion species, Brewster windows may be necessary to reduce reflection losses. These windows will contain the plasma and prevent mirror damage from ion bombardment.

A rectangular configuration is shown in FIG. 4. The rectangular design allows room for microwave waveguide access to the resonator region. Also, permanent magnets may be used to reduce input power requirements. The magnet poles 42 bracket the two resonator mirrors, one of which 44 is partially transmitting while the other is reflective 46. The microwave radiation enters the cavity region via waveguides 48 spaced along the length of the resonator. Gas input 50 and output vents allow control of the ion density.

The two previous designs utilized separate waveguides to feed microwave radiation to the resonator region. An alternate method to feed microwave radiation to the laser cavity utilizes a slotted waveguide to radiate power to the cavity plasma. This technique can be utilized for non-gaseous sources, as shown in FIG. 5. The solid material which will supply the proper ion species forms an electrode 62 as well as a wall of a waveguide structure. The opposite wall is a mesh grid 64 which will allow ions to exit the waveguide. A buffer gas is ionized by the microwave power introduced into the source waveguide. Bombardment of the electrode surface results in sputtered ions leaving the surface where they are ionized by electron collisions from the ECRH mechanism. These ions leave through the mesh and enter the laser cavity region along with electrons, which balance the space charge fields created by departing ions. Magnets 66 provide the necessary magnetic field for the ECRH process. A slotted waveguide 68 provides microwave power for control of the electron temperature and the production of the proper ionization states of the ions. Reflecting 70 and partially transmitting mirrors 72 form the actual laser cavity. Depending upon the ion species, Brewster windows may be utilized to reduce mirror damage and confine the plasma.

Another technique for coupling microwave energy to the plasma utilizes a resonant microwave cavity as shown in FIG. 6. The source electrode 82 has an opening to allow laser light to strike the reflecting mirror 84 without obstructions. Microwave power to operate the ion source is supplied by waveguide feeds 86. The plasma enters the microwave resonant structure 88 where the electron temperature can be adjusted for maximum laser output. The entire structure is immersed in a solenoidal magnetic field produced by current coils 90. Output laser radiation leaves via a partially transmitting mirror 92.

The potential advantages of a microwave cavity are that high peak powers can be attained on a pulsed basis, since energy is built up in the cavity. In addition, the polarization of the microwave source is not as significant as in configurations in which the microwaves are introduced normal to the magnetic field vector.

It should be noted that there are other processes besides ECRH which will allow the production and control of a plasma suitable for laser output. Direct excitation without resonant magnetic fields may be necessary for very high plasma densities or neutral densities. This is due to the electron-ion collision frequency, which when very high prevents the electrons from gaining energy in a resonant fashion. Thus very high electric fields are required to achieve ionization, since the electrons must attain the ionization energy before collisions take place.

In shorter wavelength lasers, where higher ionization states are necessary, it may be possible to control the population inversion on a given laser transition by depopulating an intermediate lower level by controlling the ion energy. Thus use of ion cyclotron resonance heating (ICRH) can be useful in microwave plasma laser design. Each ionization charge state can be influenced by a separate ICRH frequency, and thus it may be possible to selectively overpopulate a given charge state. All of these techniques are to be considered as a part of this invention. In particular, what is claimed is: