Method and apparatus of producing coherent high-frequency electromagnetic radiation by interacting beams of ions and electrons

This disclosure relates to the production of coherent waves of electromagnetic radiation, especially of short wavelengths including X rays, in the form of pulses or continuous beams, utilizing mutually interacting beams of charged particles that include positive ions and electrons. The atoms of which the ions are formed exist in states of excitation energy by virtue of their ionization. The ions capture electrons as the two beams interact, thereby becoming capable of undergoing de-excitation and emitting characteristic electromagnetic radiation. When heavy elements and a high degree of ionization are involved, the radiation so produced can be of high frequency; often X rays. The radiation energies can be of large natural widths which make conditions favorable for the emissions to be composed into a coherent pulse or beam. Despite the extremely short life times of the excited states, the required level of population inversion of the laser medium can be achieved by a specialised approach; population inversion is generated in a limited region on the laser medium, a beam of highly positive ions, by flooding the region with electrons drawn out from an adjacent beam. The population so formed in a region is advanced along the medium, region to region, in synchronization with the progress of the coherent photons. A preferred mode of the invention that generates a coherent X ray pulse of 11.2 keV photons having an energy output of 3.6 J and a power rating 360 GW is described.

FIELD OF THE INVENTION 
The present invention relates to the production of coherent electromagnetic 
radiation, especially radiation of high frequency including X rays, by the 
interaction of beams of electrically-charged particles. 
BACKGROUND OF THE INVENTION 
Electromagnetic radiation is emitted when an atom or molecule comes down 
from an upper to a lower energy state in accordance with the laws of 
quantum electrodynamics, conserving momentum and energy. In a laser, the 
best-known case of coherent electromagnetic radiation generated by atomic 
systems, this is made to occur as a resonance process via stimulation of 
excited atoms by incident photons having energy the same as that of the 
photons that result from the de-excitation. The demands of pumping, 
population inversion, stimulation, and multiplication of photon 
intensities without excessive losses, essential to the generation of 
coherent radiation can be met with relative straight-forwardness for 
radiation in the infrared and visible regions of optical frequencies. 
Various techniques were applied successfully in this effort that led to 
the development of lasers of a large range of wavelength. Special efforts 
further led to a variety of lasers and to lasers capable of very high 
power output. Several modes of soft X-ray lasers were built over the past 
years, with ionized vapors in the plasma state employed as the laser 
media. M. D. Rosen et al, Physical Review Letters, Volume 54, (1985), 
pages 106-109, describe an exploding foil technique of achieving such a 
soft X-ray laser. Despite such successes, generation of X-ray lasers has 
remained restricted to relatively low photon frequencies. 
Production of lasers of increasingly higher frequencies is beset with 
rising difficulties. For example, A. V. Vinogradov and I. I. Sobel'man, 
Soviet Physics JETP, Volume 36, (1973), pages 1115-1119, give a 
presentation of the problems visualised of creating laser radiation 
sources in the far ultraviolet and X-ray regions. Energy-input demands are 
higher at increased radiation frequencies. Population inversion cannot be 
maintained for long enough periods because the rate of spontaneous 
emission relative to stimulated de-excitation increases as the third power 
of frequency of the emitted radiation. Only excited states of ultra short 
life times have large enough energy widths that provide adequate resonance 
cross sections for stimulated emission. Conventional reflection techniques 
do not apply for X-ray wavelengths. Consequent of these difficulties, the 
lasers built hitherto are limited to wavelengths over a few nm, which 
correspond to photon energies below about 1 keV. 
In view of the great significance of X-ray lasers in science, technology, 
and medicine, persistent efforts continue to be undertaken for developing 
lasers operating at higher photon energies. In illustrating this, D. L. 
Mathews and M. D. Rosen, Scientific American, December 1988, pages 86-91, 
review various efforts undertaken in laboratories worldwide for producing 
X-ray lasers of short wavelengths. Also, W. T. Silfvast, Selected Papers 
on Fundamentals of Lasers, SPIE Milestone Series, Vol. MS 70 (SPIE Optical 
Engineering Press, 1993) presents a more recent account of such ongoing 
efforts. 
SUMMARY OF THE INVENTION 
The present disclosure envisages the production of coherent electromagnetic 
radiation, particularly of photon energies higher than 1 keV, based on the 
characteristic high-frequency emissions of atoms, especially the heavier 
atoms. The core levels of the atoms which account for such high-energy 
photons have remarkably short life times, often much shorter than a 
femtosecond, so that the levels have natural widths that are in the range 
of several eV's. In a medium of atoms which are fully or highly ionized, 
individual atoms allowed to interact with and capture low-energy electrons 
as proposed in the current disclosure may emit a cascade of photons 
representing the characteristic emissions of the ionized atoms, as the 
captured electrons tend to go into the lowest energy states available. If 
the ions that emit these photons are not having a wide distribution of 
velocities, the Doppler broadening of the radiation emerging in a specific 
direction can be small compared to the large line widths. Further, the 
energy shift of the emitted photon resulting from the recoil due to 
emission or absorption of the photon can be negligible relative to the 
line width. The recoil effect on the ion due to capture of a low-energy 
electron can be of similarly little consequence. These factors make the 
characteristic short-wavelength radiations of elements including X rays 
particularly amenable to resonance interaction, and likely subjects 
thereby for the production of coherent X-ray pulses or beams via the 
process of stimulated emission. 
Among the crucial factors deciding on the usability of a certain element 
for production of coherent electromagnetic radiation of a desired 
wavelength are the energies of the characteristic emissions and their 
natural line widths. The line widths increase for the elements sharply 
with increasing value of the atomic number, and can be large for 
medium-heavy and heavy elements. For example, the energy width of the 
K.sub..alpha.1 line is known to be 11.2 eV for Sn, and 103 eV for U, the 
heaviest stable element (see Table 1). Thus, while uranium which provides 
the highest-energy characteristic radiations may be preferred for hard X 
rays of photon energy .about.100 keV, other elements may also be usable 
while coherent radiation of lower-energy photons are sought. 
TABLE 1 
______________________________________ 
The photon energies and the natural line widths of 
two prominent characteristic emissions, K.sub..alpha.1 and 
L.sub..alpha.1, of 
selected medium-heavy and heavy elements. 
Atomic Emission Energy 
Line Width 
Element 
Number K.sub..alpha.1 
L.sub..alpha.1 
K.sub..alpha.1 
L.sub..alpha.1 
______________________________________ 
Ni 28 7.5 keV 0.94 keV 
3.0 eV -- eV 
Se 34 11.2 1.49 4.1 -- 
Sn 50 25.3 3.75 11.2 2.62 
Au 79 68.8 11.61 62.5 7.85 
U 92 98.4 17.45 103.0 12.40 
______________________________________ 
In the present case, wherein lasing of the characteristic emissions of 
atoms especially arising from the core shells is aimed at, the demands on 
pumping effectively mean that the atoms of the medium must be highly or 
totally ionized. Ordinarily, when an assemble of atoms of an element are 
ionized by a conventional method such as thermal collisions or interaction 
with electrically-charged particles or supply of electromagnetic energy or 
any standard means, the ionization of the atoms is accounted for by the 
removal of outer electrons only. The removal of core electrons from the 
atoms, necessary to acquire a high degree of ionization is hard to 
achieve, especially while heavy atoms are targeted; and requires an 
intensified application of any of the conventional techniques of ionizing 
atoms. Alternately it can be accomplished with good effectiveness by a 
direct process based on the in-flight annihilation of positrons. Intense 
levels of ionization in heavy elements can be made possible through this 
method. The method has been described in detail in a U.S. patent 
application filed by Jose C. Palathingal, pending consideration of the 
U.S. Patents and Trademarks Office (application Ser. No. 09/096,314 dated 
Jun. 11, 1998). The positron-annihilation process eliminates 
preferentially the core electrons of the atoms. The technique can be 
applied to heavy atoms with greater ease if they have been already ionized 
to lower degrees by a conventional technique. 
A vacant core-electron level in an ionized atom can be filled by having an 
electron available for occupying the vacancy. An electron of a higher 
shell of the same ionized atom can move into the vacant level. 
Alternately, an electron can be transferred from another nearby atom or 
ion. A yet another possibility is that a free electron can be captured 
from the vicinity. In this disclosure, it is proposed that, in a preferred 
mode, capture of electrons into vacant states of ions be made possible by 
allowing the ions to interact with a high-density influx of electrons of 
appropriate energy. 
In the method of the present invention, owing to the extremely short life 
times of the excited energy levels, and the consequent practical 
difficulty of obtaining and maintaining a large assembly of totally or 
nearly totally ionized atoms, a steady population inversion essential in 
the production of coherent radiation is achieved by special means. A 
photon traversing the laser medium can cause a stimulated emission from an 
atom in its path only if the instant of arrival of the said photon at the 
position of the said atom lies within the short life time of excitation of 
the subject atom. The effort is hence directed presently towards 
generating at a time, in a small region, a localised population inversion 
which may last there only very shortly, but such region of population 
inversion is made to shift continuously in a sequence, region to region 
along the length of the medium in synchronization with the advance of the 
stimulated radiation in the same direction. Thus in the present method, 
the provisional region of laser activity varies progressively along the 
length of the laser medium. A parallel approach was employed by John J. 
Shipman, Jr., Applied Physics Letters, Volume 10, (1967), pages 3-4, for 
deriving an increased power yield from neon and nitrogen lasers. In this 
approach, a wave of current excitation travels along the laser medium with 
a velocity matching that of stimulated emission. 
An illustration may be made citing the case of the K.sub..alpha.1 
-characteristic radiation of atoms. Since the K.sub..alpha.1 radiation 
arises from the transition of a L.sub.III electron to a K level, the 
population inversion relevant to the K.sub..alpha.1 case is described as 
the state having one or more electrons occupying the L.sub.III level of 
the ions while the K shell has at least one vacancy. This description 
suggests that an inverted population can be made possible at any location 
of a medium of totally ionized atoms only provided that an adequate number 
of ions of the region capture electrons into the L.sub.III level. A 
captured electron can remain in the L.sub.III state for only a short 
period, typically .about.10.sup.-16 s or less for a medium-heavy or heavy 
element, before it is transferred into the K vacancy. It is hence 
imperative that in order that a stimulated K.sub..alpha.1 emission be 
possible from an ion, the said ion be found in the above-defined excited 
state when a photon of resonance energy interacts with it. 
The method of this disclosure is hence outlined as follows. A limited small 
region of the laser medium consisting of ions in the form of totally or 
nearly totally ionized atoms is irradiated by an assemble of electrons 
located aside, forcibly deflected toward the laser medium by a progressive 
force field which can be electric or magnetic in character. The force 
field advances in the direction parallel to the laser medium so that 
region after region of the medium can be irradiated by electrons, the 
region being subjected to irradiation varying along the length of the 
laser medium from end to end at a required constant pace of time. The time 
interval between the instants that the electron influx hits the two ends 
of the medium is matched with the time of flight of photons between the 
ends. During the irradiation by the electrons, some of them are captured 
by the ions. The captured electrons end up in the lowest available 
vacancies, which are in the K shell in the case of totally-ionized atoms. 
Emissions are hence initiated at one end of the medium and some of the 
photons proceed in the direction towards the other end of the medium. The 
progress of electron irradiation and the corresponding continuous advance 
of population inversion from region to region along the length of the 
medium, governed by the speed of progression of the deflector field, is 
synchronized with the advance of these photons. A number of the photons 
moving along the medium are therefore likely to encounter ions immediately 
after electron capture, before spontaneous de-excitation of the ions could 
take place. This can initiate a chain process of stimulated emission that 
represents laser action in the medium. 
Despite the possibility of creating stimulated emissions in a cascade 
process as afore-said, the actual feasibility of a coherent pulse or beam 
depends quantitatively on the relative magnitudes of the 
stimulated-emission cross section and the total cross section for photon 
scattering and absorption. Scattering and absorption are commonly 
dominated by atomic or electronic processes. If the medium is fully or 
very highly ionized, and no free electrons are present, the cross sections 
for varied scattering and absorption processes related to electrons can 
each be negligible or nil. Viewed quantum-mechanically, for example, an 
atom devoid of any electron cannot initiate the Compton-scattering 
process. Photoelectric absorption and the Auger effect also require that 
bound atomic electrons be available that can absorb photons. Coherent 
scattering by the whole atom is not present when the atom is fully devoid 
of electrons. However, coherent scattering by the nucleus via the Thomson 
or the Delbruck process can occur owing to the interaction of the photon 
with the nuclear field. This cross section can indeed be very small 
compared to the resonance cross section which accounts for stimulated 
emission. Coherent scattering by highly ionized atoms could have only a 
comparable role. 
At resonance energy, the cross section for stimulated emission is given by 
the well known formula, 
EQU .sigma..sub.0 =(.lambda..sup.2 /2.pi.).multidot.g.multidot..GAMMA..sub.i 
/.GAMMA. 
wherein .lambda. stands for the photon wavelength. And, g represents the 
spin-statistical weight ratio, .GAMMA..sub.i the partial energy width of 
the excited state for the transition of interest, and .GAMMA. the total 
width of the state. Where a single photon transition dominates the decay 
of the excited state and non-radiative transitions are nearly absent, this 
ratio could be almost unity. When the incident photon energy, E is 
distinct from the resonance energy E.sub.0, the cross section is reduced 
to 
EQU .sigma.(E)=.sigma..sub.0 /.vertline.1+4(E-E.sub.0).sup.2 /.GAMMA..sup.2 
.vertline. 
In actuality, the effective average cross section, .sigma..sub.eff for 
stimulated emission is smaller than .sigma..sub.0 because of broadening of 
the energy of the incident photon owing to various recoil and Doppler 
processes. However, in the case of characteristic high-frequency emissions 
of atoms, the variations in photon energy due to recoil-energy shift and 
Doppler effect can be each much smaller than .GAMMA.. In such a case, the 
maxiumum cross section .sigma..sub.0 can become applicable. 
Conditions of large stimulated-emission cross section and low photon 
absorption can be met by the method of the invention, a preferred mode of 
which is detailed below.

DETAILED DESCRIPTION OF THE INVENTION AND A PREFERRED EMDODIMENT 
A preferred mode of the method and the apparatus is now described citing a 
medium-heavy element, selenium which has atomic number 34 and mass 78.96 
atomic units as the laser material. 
T represents a high-vacuum tube of nonmagnetic material, (see FIG. 1), with 
a fixed axis of symmetry defined as the x direction. Two beams of 
electrically-charged particles, P and S are transmitted simultaneously 
through the tube along paths parallel to the tube axis. The beam P, 
hereinafter referred to as the primary beam, consists of totally-ionized 
monoenergetic selenium atoms and monoenergetic free electrons, and is 
composed of a plurality of beams of selenium ions and electrons which 
overlap over a specified path across a range of distance marked PP in FIG. 
1. This composite primary beam has a square cross section, 0.1 mm wide in 
zx plane and 0.1 mm thick in the xy plane. In the preferred mode, the beam 
S, hereinafter called the secondary beam consists of free electrons and 
protons. It is also composed of a plurality of beams made to overlap over 
a specified path across a range of distance marked SS. This latter 
composite beam has a ribbon-like rectangular cross section of width 0.1 mm 
parallel to the zx plane and thickness 10.sup.3 A.degree. along the xy 
plane. The two composite beams, the primary and the secondary, thus have a 
pair of sides of width 0.1 mm mutually parallel and facing each other. 
They are separated by a gap G of width 1500 A.degree.. 
In the preferred mode, the net electric charge of each of the two composite 
beams is set zero. Also, the net electric current of each beam is made 
zero. By having the net charge zero, the presence of net electrostatic 
repulsive force within the particle confines is avoided. Thus, the number 
density of electrons in the primary beam shall be set to be 34 times 
larger than that of the Se ions. The kinetic energy of the selenium ions 
is 34.0 keV and that of the electrons 1.631 MeV. The Se ions all move in 
the same direction, left to right according to FIG. 1. With close to 
50.05% of the high-speed electrons moving in the direction the same as of 
the Se ions, and the rest, slightly fewer, moving in the opposite 
direction, the net current of the primary beam is made zero. It may be 
noted here that at the set ratio of energies of the Se ions and electrons, 
the momenta of the particles are proportional to their charges, so that 
the relatively heavy ions and the light electrons can have the same 
curvature of motion in any common transverse magnetic field. With the net 
electric current of the beam zero, no self-generated magnetic field loops 
surround the beam, which may tend to reshape the beam through the pinch 
effect. The secondary beam is constituted to provide for a net charge and 
current both zero, by having the total numbers of electrons and protons in 
the beam equal, and equal numbers of electrons passing in opposite 
directions, and, similarly, equal numbers of protons passing in opposite 
directions. Both types of particles are of kinetic energy 100 eV. This 
composite beam of low-energy particles also is free of any self-generated 
pinch effect. 
It is to be particularly noted here that the two particle beams, being 
composed of oppositely-charged atomic constituents, can lose intensity by 
recombinations and collisions. Recombination losses are not expected to be 
significant however since the kinetic energies of the electrons that are 
constituents of the primary and secondary beams are too high to present 
large electron-capture probabilities for the respective positive ions of 
the respective beams. Applying a longitudinal magnetic field over the 
beams can help in reducing particle losses by collisions. In the preferred 
mode, this field has a strength 10 T, and is created by an electric 
current passed through a superconducting solenoid symbolically represented 
by the coil o wound over the beam tube T (FIG. 1). 
The production of coherent radiation shall be based, in the preferred mode, 
on the K.sub..alpha.1 emission of selenium, to be undertaken utilizing a 
linear section of the primary beam. This section, marked C.sub.0 D.sub.0 
in FIG. 1, is referred to hereinafter as the laser medium. The process of 
population inversion is initiated at a small region around D.sub.0 of this 
column by deflecting electrons from a small region around D of the 
secondary beam towards a small region around D.sub.0 by a transverse 
electric field or field component acting along the y direction. The field 
is oscillatory and progressive, travelling in the direction D to C at the 
speed of electromagnetic waves. The field vector polarizes the secondary 
beam containing electrons and protons, and causes transverse charge 
displacements, resulting in charges being expelled in opposite directions. 
Electrons can thus be propelled towards the laser medium containing Se 
ions, and irradiate the ions. The progression of the field causes the 
region of irradiation advance along with the field. The electron-capture 
process initiated at D.sub.0 is thus moved steadily to the end C.sub.0 at 
a pace that causes the photons from the initiating region around D.sub.0 
arrive at any region along the length of the ion column in synchronization 
with the development of population inversion in the region. 
The required electric field can be generated, in principle, by any known 
method of producing a progressive electric field of the required strength, 
including a plane-polarized laser beam. In the preferred mode, provision 
is made to have a powerful externally-derived laser pulse denoted L (see 
FIG. 2) to be swept over at the speed of light along the length of the 
secondary beam, incident at 30.degree. inclination on the 0.1-mm wide 
broad side facing away from the primary beam. This laser pulse is of an 
infrared wavelength of approximately 106,000 A.degree.. The geometrical 
cross section of the pulse is defined by a 3 mm.times.3 mm slit N (as in 
FIG. 3). Diffraction broadens the cross section, but the pulse is 
refocussed by a double-curvature focussing device F into a reduced 
rectangular cross section 0.1 mm.times.0.05 mm before being incident on 
the secondary beam. With the angle of incidence 30.degree., a narrow 
section of the beam, 0.1 mm.times.0.1 mm, is exposed to the laser pulse at 
a time. The sweep of the pulse is made possible by means of a 
fast-rotating plane reflector, R rotating at a precise pre-determined 
speed. In the preferred mode described herein, the laser pulse is incident 
along the direction NR and reflected by R towards a fixed plane mirror M, 
which directs the pulse to a point on the section DC of the secondary 
beam, S. In this mode, the beam sections DC and D.sub.0 C.sub.0 are of 
length 20 cm. For its entire path, the travel plane of the incident laser 
beam is parallel to the xy plane. The rotational direction of the mirror R 
is such that the point of laser incidence on the secondary beam moves in 
the direction D to C. The fixed mirror M is located near to the beam 
section DC. The rotational speed required is determined by the path 
lengths of the laser beam, and the angles of incidence of the beam on the 
fixed mirror M and on the secondary beam. The distance RM is taken as 200 
m. Accordingly, the rotational speed of the mirror R is about 60 kHz. With 
curved mirrors substituting for plane mirrors, the rotational speed 
required can be greatly reduced. The mirror supports are required to be 
strong enough to be able to absorb the momentum impulse generated by the 
reflection of the incident radiation. By ensuring that the radiation is 
incident on the surface of the rotating mirror symmetrically about its 
axis, development of a torque that may affect the rotational movement can 
be avoided. 
The plane of polarization of the laser pulse L shall be parallel to the xy 
plane. The amplitude of the oscillating electric field of the laser pulse 
should be large enough so that the electrons of the secondary beam may 
achieve an adequate transverse speed within a time interval of one half 
wave period and proceed to be injected well into the primary beam. At a 
kinetic energy 300 eV, the electrons have a speed 10.sup.9 cm/s, and shall 
be able to penetrate the ion beam adequately. The intensity of the laser 
pulse is hence preset, as detailed subsequently, to enable the electrons 
receive adequate kinetic energy so that they move on outward with an 
average speed 10.sup.9 cm/s. 
The density of selenium ions in the primary beam P that constitutes the 
laser medium is set to be 2.times.10.sup.8 /cm.sup.3. Correspondingly, 
electrons of the beam have density 6.8.times.10.sup.9 /cm.sup.3. Thus, the 
beam contains 2.times.10.sup.14 ions and 6.8.times.10.sup.15 electrons per 
cm length. The secondary beam provides the low-energy electrons to be 
captured by the Se ions of the primary beam, and the required electron 
density of the secondary beam shall therefore be determined on the basis 
of the probability of electron capture per Se ion. Reliable experimental 
data on the capture of electrons by highly or totally ionized atoms 
applicable to the present case are not available. A rough estimate is made 
herein however from classical and semiclassical considerations. This is 
done by considering the probable capture of a free electron by an ionized 
atom into a vacant atomic shell, the free electron having kinetic energy 
much less than the kinetic energy the electron would have if captured into 
the shell and established a stable orbit. It is assumed for simplicity 
that, in a collision with an atomic nucleus, if the finite time such an 
electron spends within the orbital distance of a particular shell of the 
atom is equal to at least one period of orbital revolution, the electron 
will be captured into the orbit. For lesser time spent in the vicinity, 
the capture probability is proportionately less. The collision frequency 
is obtained by an approach analogous to the kinetic theory of gases. The 
L-orbit radius of a selenium atom is roughly 0.06 A.degree., and the 
period of revolution of the L electron of the Se atom is 
1.6.times.10.sup.-18 s. It takes .about.1.2.times.10.sup.-18 s for an 
electron of kinetic energy 300 eV to traverse past an ion within the 
proximity defined by the L radius. Based on this approach, the minimum 
electron density required of the secondary beam so that a Se ion of the 
primary beam may have a 20% chance of capturing an electron into any of 
the eight L subshells directly per time interval 1.6.times.10.sup.-16 s, 
the life time of a K vacancy while the L shell is fully occupied, is 
determined to be .about.2.times.10.sup.23 /cm.sup.3. 
Together with the protons which shall have the same numerical density as 
the electrons, the secondary beam constitutes a high-density plasma, 
electrically neutral as a whole. The dense composition of the secondary 
beam demands that the incident infrared laser pulse shall have a 
correspondingly high energy density, so that the electrons may pick up 
average energy .about.300 eV in one half wave period as the pulse 
traverses the beam. Compared to the electrons, the protons absorb little 
energy. Owing to the high particle density involved, it is expected that 
the net energy absorbed by the particles can be rapidly redistributed. 
Estimates show that, with radiation losses included, the required minimum 
energy of the laser pulse at incidence shall be roughly 40 J per cm 
length. The corresponding power rating is .about.1.2 TW. 
The electric field of the intense infrared laser pulse propels electrons 
out of the secondary beam in either lateral direction depending on the 
phase of the wave front at incidence (see FIG. 4). Because of their larger 
mass, the protons are not projected significantly beyond the confines of 
the beam. During the first wave period after the wave front is incident at 
a point on the secondary beam, a batch of electrons of the beam are 
deflected laterally towards the primary beam. The field begins to be 
reversed at the end of a half period, but the electrons shall continue to 
move on, although with reducing speed (FIG. 4c). By the end of a full 
period, the velocity is reduced to zero. The velocity is not however 
reversed during a full cycle, but undergoes a periodic variation, going 
from zero to a maximum and back to zero. The next wave period shall hence 
advance the electrons into the medium still further (FIG. 4d). It is 
assumed herein that the laser-pulse intensity remains constant. If 
however, the electric field is attenuated significantly by energy 
absorption during the first period, the electrons could continue to move 
on thereafter with a speed reduced little from the maximum acquired during 
the initial time interval. In the preferred mode, at the incident energy 
40 J/cm, the beam intensity is reduced by only about 5% within the first 
half period. Hence, for simplicity, it is assumed that the electrons 
continue to move on with an average speed 10.sup.9 cm/s. It is to be 
expected that an equal number of electrons are deflected in the reverse 
direction. Secondary effects are ignored in this picture, including the 
effects of interaction of the nonuniform transverse magnetic field of the 
laser pulse with the moving electron charge and the electron magnetic 
dipole moment. Since the speeds of the electrons and protons of the 
secondary beam are much smaller than the speed of light, the magnetic 
field vector has a considerably lesser role on the motion of these 
particles compared to the electric field vector. 
The probable role of external fields such as magnetic confinement fields 
that may be part of the system maintaining the particle beams and may 
extend into the region of the present apparatus, not specified in this 
disclosure, is not discussed herein; but is not expected to be an 
unavoidable hindrance to the technique of the invention. 
Among the toughest problems to be normally expected in the production of 
high-frequency coherent radiation shall be the huge pumping powers 
required for creating a population inversion, and removing the heat 
produced in the laser medium. In the present method, the laser medium 
consists of totally or nearly totally ionized atoms, and the process of 
production of coherent radiation involves flooding the medium with 
low-energy electrons at very high densities which may, in principle, 
generate a significant amount of heat over the medium having only a 
minuscule heat capacity. The build up of thermal energy can result in a 
total or a partial disruption of the beam in the irradiation region and 
consequently in total stoppage or reduction of coherent photon emission. 
This aspect of adverse thermal effects over the primary beam therefore 
needs to be looked into quantitatively. 
Collisions occurring between the incident 300-eV low-energy electrons of 
the secondary beam deflected into the primary beam and the Se ions of the 
primary beam involve little energy transfer, and although several 
collisions are involved within the time period .about.10.sup.-14 s over 
which a selenium ion is subjected to irradiation by the electrons, the net 
energy exchange could be only .about.1 eV, quite small compared to the 
kinetic energy of the ions; and of little consequence as revealed 
subsequently. 
The energy transfer involved in collisions between the 1.631-MeV electrons 
of the primary beam and the incident 300-eV electrons could be 
approximately estimated on the basis of an analogy with the loss of 
kinetic energy of 1.631-MeV electrons in transit through a solid material 
medium of light atoms. The electron density for such an atomic medium is 
.about.10.sup.24.cm.sup.-3, several times larger than the incident density 
of low-energy electrons. The specific energy loss for electrons of energy 
1.631 MeV is .apprxeq.1.5 keV/mg.cm.sup.-2 for the medium. The effective 
distance a primary-beam electron travels through the dense cloud of 
low-energy electrons of the irradiation region depends on the dimensions 
of the irradiation region at a time. The average electron density that the 
primary beam is being flushed with in the irradiation region at any 
particular instant of time is around 10.sup.23 /cm.sup.3, and the 
effective average distance across which a 1.631-MeV electron has to 
transit under irradiation by the incident low-energy electrons is 
.about.3.times.10.sup.4 .ANG.. Accordingly, the 1.631-MeV electron is 
subjected to an average net energy loss .about.1 keV in collisions with a 
large number of low-energy electrons. This energy transfer shall not be 
expected to significantly affect the motion of the Se ions of the region 
of population inversion and be a hindrance to the production of coherent 
photons from the region. 
The primary beam may absorb energy from the infrared laser pulse that 
emerges from the secondary beam with attenuated intensity. The heavy Se 
ions pick up little kinetic energy, but the 1.631-MeV electrons of the 
beam may be expected to receive substantially more, .about.100 eV. As 
stated above, a modest variance of the energy of these electrons is not 
expected to be a hazard of consequence. 
Thermal energy can be built up in the primary beam, the laser medium by 
absorption of a part of the large flux of low-energy photons generated by 
the acceleration that the charged particles of the two beams may undergo. 
However, few of these photons can be absorbed inelastically in the laser 
medium as no appropriate quantum states are available in significant 
numbers. Elastic collisions of these photons can produce little energy 
transfer. Photons generated during electron captures by the Se ions can 
also contribute to the build up of thermal energy in the primary beam. But 
these photons are relatively few and the thermal contribution is not 
expected to be large. 
Overlap between the time instant when a photon emitted by a Se ion arrives 
at the position of another Se ion of the laser medium and the duration for 
which the latter ion is found in the required specific state of population 
inversion is crucial in achieving a viable yield of coherent photons. 
There can be variations in the duration of interaction of an ion with a 
low-energy electron prior to capturing it, and in the interval an ion may 
remain in the excited state before being spontaneously de-excited. The 
incident low-energy electrons may arrive at any particular depth within 
the laser medium after a degree of straggling caused by interactions with 
the ions and electrons present in the medium. This straggling increases as 
the electrons penetrate deeper. Besides affecting the probability of 
capture, unregulated propulsion of electrons could lead to erratic 
intensity and timing of irradiation. Such factors need to be taken into 
account in estimating the effective degree of time synchronization at a 
region between the incoming photons and the build up of population 
inversion. 
The time-jitter between the occurrances of the two independent events, 
emission of a first photon by a Se ion at one point of the laser medium 
and the subsequent stimulation emission of a second photon by another ion 
located at another point promoted by the oncoming first photon, both 
governed by a common time constant, lowers the degree of synchronization 
between the two events. This may be accounted for by a net reduction 
factor .apprxeq..sqroot.2 in the estimate of the effective population 
density. The varied features of erratic irradiation cited above could be 
taken into account in principle in terms of other reduction factors over 
the effective population density. For a thin layer at the surface of 
electron entry into the primary beam, the laser medium, these individual 
reduction factors may not be large, and a combined factor 2 may be 
accepted as allowing for all the varied effects. The net reduction factor 
is hence taken as 2.sqroot.2; roughly as 3. This net factor may be 
expected to increase for layers of the laser medium at greater depths of 
electron penetration. On the other hand, the density of inverted 
population may tend to rise with increasing depth owing to the reduced 
speed of the electrons and the corresponding rise in electron-capture 
probability. It may hence be assumed for simple calculations that the net 
effective inverted population density is constant across the thickness of 
the laser medium within the range of the incident low-energy electrons. 
This range is estimated to be .apprxeq.0.1 mm; the full thickness of the 
primary beam. Thus the production of coherent photons occurs over the 
whole laser medium. 
Free electrons may be captured into the L.sub.III subshell directly or via 
any one of the higher shells. As the captured electrons move downward from 
levels above L.sub.III into the lowest available vacant state, a large 
number are bound to transit through the L.sub.III level, which accounts 
for a significant fluorescence-yield factor among the L-X ray series. This 
effect of the upper shells which could somewhat contribute to the 
production of coherent photons is however not considered because captures 
into electron levels above L.sub.III are expected to be relatively few due 
to the kinetic energy .about.300 eV of the incident electrons. Many of 
these cascades may further involve time delays considerably larger than 
1.6.times.10.sup.-16 s, the life time of the state of inverted population 
of the present case. Direct capture of electrons into the K shell from 
shells higher than the L shell and from the continuum is also ignored. 
These capture events may lower the degree of available population 
inversion, but the occurrance rate of these events too shall be small; 
estimated to be roughly 5% of the rate of capture into the L shell. 
The effective cross section for stimulated emission, .sigma..sub.eff is 
reduced by shift and broadening of the incident photon energy. The shift 
arises from ion recoil at photon emission, and the broadening from Doppler 
effect generated by velocity spread of the ions. Each of the major factors 
is considered below, and recognised to be not a serious problem in the 
method of the invention. 
The natural width of the K.sub..alpha.1 line of selenium having photon 
energy 11.2 keV targeted presently for the production of coherent 
radiation is 4.1 eV. The actual figures are somewhat different because the 
electron-screening effect of atoms that gives rise to differences in 
energy levels and level widths between ions and atoms is not considered 
herein. The recoil energy of emission of a 11.2-keV photon by a Se ion is 
only 8.5.times.10.sup.-4 eV, far smaller than the line width, 4.1 eV, so 
that the effect of this recoil on the cross section for stimulated 
emission can be ignored. 
A Se ion can be subjected to recoil on account of the capture of a 300-eV 
electron incident on it. This may lead to a variation in the velocity 
vector of individual ions. The ions could undergo a broadening of velocity 
owing to various collision processes also. Each process contributes to the 
Doppler width of the emitted photons. In order to evaluate the extent by 
which an individual process of Doppler broadening affects the resonance 
cross section, a criterion is set in terms of an energy width fraction 
defined as .GAMMA./E.sub..gamma., wherein .GAMMA. is the natural width of 
the K.sub..alpha.1 line of selenium and E.sub..gamma. is the 
K.sub..alpha.1 -photon energy. This fraction has value, 
3.66.times.10.sup.-4 in the present case. If a recoil or scattering 
process results in a velocity shift the ratio of which to the speed of 
light is much less than the width fraction cited above, the corresponding 
Doppler effect has only negligible effect on the resonance cross section. 
Following this approach, the recoil of a Se ion resulting from the capture 
of a 300-eV electron is expressed in terms of the ratio of the recoil 
speed v.sub.re to the speed of light c as v.sub.re /c, which has the value 
3.times.10.sup.-7. It is thus evident that the recoil involved herein has 
little effect on the cross section of interest. It is also evident that a 
single collision event involving a Se ion and a 300-eV electron can have 
no significance. Multiple collisions that can occur also cannot have a 
serious effect since the number of such collisions that an ion may go 
through before a stimulated emission may occur during the period of 
electron irradiation, although substantial, is not large enough. The 
collisions the Se ions may undergo with the high-energy electrons that too 
are constituents of the primary beam also need to be considered. A head-on 
collision between a 1.631-MeV electron and a 34-keV selenium ion can 
produce only a 6 percent change in the momentum of the ion. The speed 
v.sub.i of a 34-keV selinium ion is given by v.sub.i 
/c=9.6.times.10.sup.-4, and thus the maximum Doppler shift a collision as 
above can produce is of a small factor, 6.times.10.sup.-5, significantly 
smaller than the width fraction of the photon. Such collisions are also 
rare; at the electron density of the primary beam, 6.8.times.10.sup.19 
/cm.sup.3, the mean free path for such ion-electron collisions in which 
the electron-scattering angle is 90.degree. or larger is found to be 
roughly 5 m. Small-angle scatterings are much more abundant, but their net 
effect is only comparable. Although the differential cross-section for 
small-angle scatterings increases as sin.sup.-4 (.theta./2), wherein 
.theta. is the angle of scattering, consideration of the solid-angle 
factor sin(.theta.) and the transferred momentum component shall show that 
the net velocity spread arising from the large number of random 
small-angle collisions is only of the same order as for collisions 
involving large angles. Ion-ion collisions do not cause a significant 
velocity spread either. Despite the large cross sections involved, that 
can be calculated using the Rutherford formula, ion-ion collisions may 
occur only as a second-order effect as they depend on the presence of a 
relative velocity between the ions. Such a relative velocity can be 
developed by and large only through the collisions involving the 1.631-MeV 
electrons, and is small as seen above. With all varied processes 
considered, involving other ions, electrons and photons, the maximum 
possible randomized variation in the kinetic energy of a Se ion is found 
to be less than .about.10 eV. The random energy is equivalent to thermal 
energy, and the resultant effect may be expressed by a thermal speed 
ratio, V.sub.th /c. At 10 eV, the ratio is found to be around 
1.6.times.10.sup.-5, too small to be significant. In fact, any thermal 
energy of the Se ions less than 1 keV produces negligible broadening of 
the photon energy in the present case. 
The above considerations reveal that the photon energy shifts and 
broadening resulting from various processes, collisions, thermal effects, 
etc. are small enough not to reduce significantly the resonance cross 
section from the theoretical maximum value. The wavelength, .lambda. of 
the 11.2-keV K.alpha..sub.1 emission of selenium being 1.107 A.degree., 
this maximum value of the resonance cross section .sigma..sub.0 is 
3.9.times.10.sup.7 b. Despite this large value of .sigma..sub.0, 
determining the availability of coherent photons from the method requires 
an analysis of photon absorption processes and the density of population 
inversion in the medium. 
With only captured electrons present in the Se ions, the atomic absorption 
processes can be small; accountable to the air molecules left over in the 
high-vacuum beam tube at a finite pressure and to the few captured 
electrons present in the Se medium. At the residual air pressure, 
10.sup.-9 torr presumed for the beam tube in the preferred mode, air 
molecules have a density .apprxeq.4.times.10.sup.7 atoms/cm.sup.3. The 
total absorption cross sections for nitrogen and oxygen are around 100 b 
per atom at 11.2-keV photon energy. Thus at the molecular density referred 
to above, far too small compared to the ion density of the beam, the air 
molecules can have little role in photon absorption. Photon absorption by 
the bound electrons can be more significant and calls for a closer 
analysis. 
Bound states can be formed in the Se ions by capture of the 300-eV 
electrons into the K or L shells, etc. The 11.2-keV K.alpha..sub.1 photons 
do not however have adequate energy to displace K electrons from the Se 
ions beyond the L shell; into higher shells or the continuum. These 
photons may however be capable of electron ejection from the L and higher 
shells by the photoelectric effect or the Auger process. Since this mode 
of photon absorption is accounted for predominantly by the L electrons and 
the cross section per electron is only a very small fraction of the 
maximum resonance cross section, the overall photon absorption caused by 
the bound electrons is negligible. The Thomson cross section accounting 
for photon scattering by the selenium nuclei, estimated as described 
earlier is .about.10.sup.-5 b, also too small to be significant. Coherent 
scatterings by Se ions having one or a few captured electrons could be 
rare events only, and may be ignored. Compton scatterings from the 
1.631-MeV electrons which have a 34-times larger numerical abundance than 
Se ions in the medium is more substantive. The cross section per free 
electron calculated on the basis of the well known Klein-Nishina theory is 
0.64 b. With the electron density taken into account, this corresponds to 
a mean free path .about.250 m, much longer than the laser medium. 
Higher-order processes such as inverse bremsstrahlung are ignored as being 
only rare events. Thus, interactions with high-energy electrons are not 
expected to cause significant photon absorption. 
The low-energy electrons injected into the laser medium and are present in 
large numbers may contribute to scattering of the 11.2-keV photons 
significantly. These electrons can be present in the region of irradiation 
at a density, 2.times.10.sup.23 /cm.sup.3 Since electrons are dispersed to 
either side of the secondary beam, the average effective density is half 
the above. In effect, the presence of these low-energy electrons turns out 
to be the foremost factor of photon absorption which corresponds to an 
absorption length 16 cm. Accordingly, the photon intensity can be reduced 
by a factor 2 over a medium length 11 cm. 
The electron density flooded through the primary beam is expected to be 
adequate to enable 20% of the ions capture an electron into the L shell 
within 1.6.times.10.sup.-16 s. It is considered that roughly 50% of the 
events are accounted for by the L.sub.III subshell. Taking into 
consideration the average net reduction factor 3 assumed above and the 
dispersal of irradiation electrons to either side of the secondary beam, 
an effective inverted population .apprxeq.1.7% may be assumed. This means 
that as electron irradiation advances along the length of the medium in 
synchronization with the advance of de-excitation photons, 1.7% of the 
ions in the path of a photon travelling parallel to the length of the 
medium are seen to be with an electron in the L.sub.III level and a 
vacancy in the K shell. Since, as seen above, the electronic absorption is 
modest and the line broadening is small compared with the natural line 
width, the effective cross section for stimulated emission, averaged over 
all the ions in the path of coherent radiation (.sigma..sub.eff).sub.av is 
6.6.times.10.sup.5 b. A mean length of the medium over which the intensity 
of the coherent radiation may increase by a factor e.sup.1, termed 
amplification length may be obtained. For the present case, the 
amplification length is 7.6 mm. With atomic absorption taken into account, 
the effective amplification length is 8.0 mm. Accordingly, the medium 
length over which the laser intensity could double is about 5.5 mm. This 
result is quite satisfactory even while considering that the estimate has 
been only rough. The ratio of the absorption length to the amplification 
length shall be expected to remain fairly constant over variations of the 
electron-irradiation density of at least one order of magnitude. However, 
since the absorption length is primarily dominated by the incident density 
of low-energy electrons derived from the secondary beam, an increase of Se 
ion density of the primary beam by some numerical factor, while retaining 
the incident electron density unvaried, shall result in a reduction of the 
amplification length by roughly the same factor. 
Whereas the above considerations reveal that production of coherent 
radiation by this approach can be possible, despite a number of greatly 
demanding technical criteria that needs be met, the intensity of the 
coherent radiation produced depends additionally on a number of factors. 
In common with other lasers, the geometry and length of the lasing medium 
are extremely important. To make an estimate of the intensity of the 
coherent X-ray beam produced in the mode described, the laser medium, 
having length 20 cm and width 0.1 mm and thickness 0.1 mm, wholly 
effective in the production of coherent radiation, may be viewed as a 
series of thin linear parallel strips adjoining one another. The strips, 
20-cm long, may all be considered to have width 0.1 mm, the same as of the 
medium, and thickness 16 A.degree. which corresponds to the depth of 
penetration of the 300-eV electrons in 1.6.times.10.sup.-16 s, the life 
time of the state of population inversion. For each of these strips, thus 
having dimensions 20 cm.times.0.1 mm.times.16 A.degree., it may be assumed 
that the population inversion advances along its length in synchronization 
with the advance of photons. The number of Se ions in a single strip is 
6.4.times.10.sup.10, of which 1.7% may be considered as being in the state 
of population inversion along the transit path of coherent photons. 
With a 0.1-mm long section of the secondary beam under irradiation by the 
incident laser pulse at a time, the total duration of irradiation at any 
point of the medium is approximately 3.3.times.10.sup.-13 s. It is however 
to be expected that the duration of production of coherent photons from 
any section of a particular strip of the laser medium shall be essentially 
limited to the time of passage of the 1000-.ANG. wide band of incident 
300-eV electrons across the strip. Accordingly, the duration of emission 
of radiation is limited to an estimated .about.10.sup.-14 s. It is also to 
be expected that the intensity of emission from each strip may not be 
constant over this duration. Further, each of the strips begins 
contributing in a sequence with mutual delay, the deeper-lying strips 
beginning to radiate only later. 
Coherent wave trains may be initiated by a photon generated by spontaneous 
emission by a Se ion located at any point in a strip. The fractional value 
of the solid angle presented by the end window of the strip at C.sub.0 for 
a point near the opposite end is only 3.2.times.10.sup.-13. Consequently a 
photon produced at the start region D.sub.0 via spontaneous emission has 
an extremely low probability of being emitted in the direction towards the 
exit window. Per effective amplification length 8.0 mm of the laser 
medium, the estimated maximum number of photons that can be spontaneously 
emitted from within the corresponding medium volume, 8.0 mm.times.0.1 
mm.times.0.1 mm, is .about.3.times.10.sup.12. Consideration of the two K 
vacancies of the Se ion raises this estimate. Thus it is seen that on the 
average, one of these photons, thus initiated from a 8.0-mm long section 
of the laser medium at the start end of the medium, emerges through the 
exit window in the direction parallel to the medium. Such a wave train as 
is originated by this photon has the potential to carry the maximum number 
of coherent photons and be of maximum length. Wave trains initiated from 
points closer to the exit window shall have greater probability of 
emerging from the window, but may be composed of only fewer photons. The 
corresponding pulses carry only less energy and are of shorter durations. 
The number of Se ions that are raised to the state of population inversion 
in a single strip per time interval, 1.6.times.10.sup.-16 s is roughly 
4.4.times.10.sup.7 per amplification length; which corresponds to 
3.0.times.10.sup.7 per intensity-doubling length 5.5 mm. For rough 
estimates, it may be considered that the coherent photon yield increases 
geometrically with medium length initially, and linearly thereafter. The 
length over which the geometrical multiplication may occur is limited in 
the presently described mode of the invention to 14 cm. A single wave 
train initiated at the start end exiting through the window may hence be 
composed of a maximum of 3.6.times.10.sup.8 photons. 
Since the irradiation period at any point in the laser medium is 10.sup.-14 
s, the duration of transit of the deflected electron beam of width 
10.sup.3 .ANG. across the point, an inverted population density 1.7% 
estimated earlier lasts in every region for the above-stated period. Since 
this total duration is sixty times larger than the natural life time of 
the state of inverted population, adequate time is provided for every ion 
to go through the state of inverted population once on the average. The 
total number of 11.2-keV photons hence emitted by the medium is roughly 
the total number of ions in the medium, namely, 4.times.10.sup.15. A 
substantial fraction of these form part of coherent pulses, although only 
a smaller fraction emerges through the exit window. Simplified 
considerations give the number of coherent photons emerging from the exit 
window to be .about.2.times.10.sup.15 photons. The radiated energy is 3.6 
J. The radiation is expected to emerge over a period .about.10.sup.-11 s, 
the duration of transit of the low-energy irradiation electrons across the 
thickness of the laser medium, 0.1 mm; not considering the reduction in 
the speed of the electrons as they progress inside the laser medium. The 
average power radiated from the window is hence .about.360 GW. 
In the mode described herein, the frequency of the coherent radiation 
measured by a stationary detector is expected to be somewhat smaller than 
the emitted frequency on account of the negative Doppler shift produced by 
the motion of the 34-keV selenium ions. The Se ions are described herein 
as moving left to right (FIG. 2) whereas the coherent photon pulse is 
progressing in the reverse direction. The speed of the ions is given by 
the ratio, v.sub.i /c=9.6.times.10.sup.-4. It is hence seen that a finite 
degree of tunability of the frequency of the coherent radiation can be 
achieved in the method of the invention by providing for variation of the 
ion speed. By employing mono-energetic ions of greater variable speed, the 
degree of tunability can be enhanced. Relativistic heavy ions, for 
example, could provide coherent high energy photon beams of a large degree 
of tunability. By having the ions and the photons proceed in the same 
direction, coherent photon beams of frequencies higher than the emitted 
frequencies can be derived. 
In the description above, a particular mode has been illustrated. However, 
the present invention is not to be construed as being limited by the 
features of the said mode as described herein. Other modes of the 
invention are possible by making such variations as are known to those 
familiar in the art. Illustrative examples are cited below. 
Variations may be made to enable the laser of the invention to have a 
continued output, or a pulsed output of which the pulse could be of any 
required duration. 
Coherent radiation may be made by the present method based on any 
characteristic line of any chosen element or composites of elements; 
including X rays. 
The particle beams could have alternate constituents, and be in alternate 
chemical or physical forms or states. The beams may be produced by any one 
or more of various methods. Different methods of beam confinement and 
preservation may be engaged. The particle beams could be of alternate 
geometric configurations, or of cross sections other than the square or 
rectangular cross section of the preferred mode. The beams could be in the 
form of pulses or steady streams. They could have different relative 
displacements and/or orientations. 
The constituents of the particle beams could be moving in mutually parallel 
or antiparallel directions, and could be chosen with any proportions of 
particle density, speed, momentum or energy. 
A plurality of primary and/or secondary beams may be engaged. 
In a particular mode of the method, the particle beams could be substituted 
by assembles of particles of any one or a plurality of geometrical 
configurations. 
In other modes of the method, the de-excitation of ions could be achieved 
by electron capture from a beam of only free electrons or of bound 
electrons belonging to ions, neutral atoms or molecules. These atoms could 
preferably be light atoms. Heavier atoms may also be used. 
In another variation possible, the secondary beam could be of atoms or 
ions, and a laser beam incident on the secondary beam could be made to 
serve as a means of dissociating and/or ionizing the atoms, and/or to 
deflect the electrons toward the primary beam. 
In yet another possible variation, the particle beam or beams employed in 
the method could have zero or non-zero net electric charge and/or display 
zero or non-zero net electric current. 
Alternate cross sections and configurations of incidence for the laser beam 
providing for the deflection of electrons could be possible. In one 
possibility, the primary and secondary beam could lie in a plane different 
from the plane of travel of the laser beam, or from a plane common to the 
laser beam and the secondary beam. The beam could be derived as a single 
pulse or a plurality of pulses, or a steady radiation. Laser beams or 
pulses of alternate parameters relating to wavelength, intensity, or power 
may be used. 
Alternate devices, alternate methods, or alternate geometries can be 
engaged to reflect the incident laser beam through the desired range of 
directions. For example, curved mirrors or a combination of curved and 
plane mirrors could be employed in substitution of plane mirrors only. 
Alternate focussing techniques and devices can be applied to regulate the 
geometrical dimensions of the incident laser beam or pulse. 
In one alternate mode, the deflection of electrons on to the ions may be 
achieved by alternate means than an electric field, such as by a magnetic 
field or fields or a combination of electric and magnetic fields, 
generated by any known means. Alternately, both electrons and protons may 
be deflected toward the ion medium; for example by a magnetic field when 
the two types of particles are moving in opposite directions. It may be 
desirable in certain modes to employ one variable magnetic field or a 
plurality of seperately-variable magnetic fields for deflecting the 
particles having charges of the same polarity or opposite polarities. The 
field or fields could vary sinusoidally with time or have other time 
dependence; or can be constant in time. 
In another mode, the initiation of the production of coherent radiation at 
any point of the laser medium could be done by incidence of photons of an 
appropriate energy at the point employing an external source. 
The tunability of the coherent radiation may be regulated by providing for 
a range of variation of the speed of the ions of the primary beam. 
Coherent beams of photon frequencies higher than the emitted frequency or 
frequencies can be made possible; by providing for positive Doppler effect 
to be effective over the emission of photons. This can be accomplished 
while the ions emitting the coherent photons are made to be moving in the 
same direction as the direction of progression of the coherent photons. 
SOME POSSIBLE APPLICATIONS 
The conventional low-frequency lasers available today have found wide 
applications in numerous fields, commerce, science, technolgy, medicine 
and others. X-ray lasers, and high-frequency lasers in general, too may be 
expected to have a wide range of applications, a few examples of which are 
listed below. 
a. Studies of nonlinear optics and plasma: 
Passage of a coherent X-ray beam through an ionized medium could invoke 
changes in the plasma which have much theoretical and practical interest. 
Valuable information could be gathered on electromagnetic wave propagation 
in an ionized medium. Studies of physical changes introduced in plasma of 
varied kinds by passage of an intense radiation beam could also be 
facilitated by the availability of coherent X-rays. 
b. Studies of atoms and materials: 
The availability of a coherent X-ray beam will enable scientific studies of 
multiple high-energy photon-absorption processes in atoms. Similarly 
material properties could be investigated by use of coherent X rays. 
c. Holographic studies: 
High-resolution studies of biological samples can be made possible with 
coherent high-frequency radiations. 
d. Radiation impacting of objects and communication: 
The impact of radiation on materials and structures can produce effects 
having relevance for terrestrial and space objects. Coherent X-ray beams 
shall provide a new tool for studies of these effects. Specific potential 
applications include remote sensing, structural alteration, function 
neutralisation, and communication. 
e. Medical applications: 
Coherent X-ray pulses could be valuable in precise destruction of tumours 
and malignancies in the human body.