Abstract: A near-perfect grating rhomb enables an output beam to be diffracted to an angle offset from the input beam. The correcting grating is tipped relative to the dispersing grating to provide the offset angle. The correcting grating is further provided with a groove spacing which differs from the dispersing grating groove space by an amount effective to substantially remove angular dispersion in the output beam. A near-perfect grating rhomb has the capability for selective placement in a FEL to suppress sideband instabilities arising from the FEL.

Abstract: A device to provide high current, low emittance electron beams with a long life cathode. The device consists of an undulator 7 which provides a source of ultraviolet light 15 for an ultraviolet photocathode 8. The undulator 7 needs a supply of electrons to produce the ultraviolet light which it can get by diverting a portion of a beam from a linear accelerator 3 before E.sub.3 or after E.sub.4 the electron beam traverses a free electron laser 5. The device is self-maintaining once a source of electrons is developed but needs a start-up source of electrons. The start up source can be provided by a pulsed cathode electron gun 1 which has to be on for a short period of time until the ultraviolet photocathode 8 is operated.

Abstract: A high gain, single-pass free electron laser formed of a high brilliance electron injector source, a linear accelerator which imparts high energy to the electron beam, and an undulator capable of extremely high magnetic fields, yet with a very short period. The electron injector source is the first stage (gap) of the linear accelerator or a radial line transformer driven by fast circular switch. The linear accelerator is formed of a plurality of accelerating gaps arranged in series. These gaps are energized in sequence by releasing a single pulse of energy which propagates simultaneously along a plurality of transmission lines, each of which feeds the gaps. The transmission lines are graduated in length so that pulse power is present at each gap as the accelerated electrons pass therethrough. The transmission lines for each gap are open circuited at their ends.

Abstract: An improved free electron laser is described. The laser comprises an accelerator arranged in order to emit an electron beam along a laser emission line and a circuit loop including a curved line which traces a periodic function along a line parallel with said laser emission line in order to produce a periodic magnetic field along said laser emission line. The periodical circuit is made of a superconducting material, so that the periodical length thereof is made as short as 100 microns without compromising the strength of the magnetic field induced by the circuit.

Abstract: A fast pulsed excitation, electromagnetic undulator or wiggler, employing geometrically alternating substacks of thin laminations of ferromagnetic material, together with a single turn current loop excitation of the composite assembly, of such shape and configuration that intense, spatially alternating, magnetic fields are generated; for use as a pulsed mode undulator or wiggler radiator, for use in a Free Electron Laser (FEL) type radiation source or, for use in an Inverse Free Electron Laser (IFEL) charged particle accelerator.

Abstract: A cyclotron autoresonance maser includes an evacuated drift tube with a first end, a second end and an axis. An electron gun introduces a beam of relativistic electrons to the drift tube first end and, for example, a wiggler magnet causes the electrons to gyrate with the gyrations having relatively small radii. A magnetic field generator is provided which forces the beam of relativistic, gyrating electrons to spiral about the axis of the drift tube. The radii of the spirals is large relative to the radii of the gyrations so that the effective interaction length of the electron beam and a maser beam, having an axis substantially coincidental with the axis of the electron beam, is substantially greater than that of a relativistic electron beam and a maser beam which simply cross. A method of generating coherent radiation is also disclosed.

Abstract: A free-electron laser including one or more diffraction gratings as part of a resonator structure, to automatically compensate for resonator reflector pointing errors. The angle of reflection of radiation incident on the diffraction grating is frequency-dependent, and this permits compensation of the pointing errors by small shifts in the frequency of operation of the laser, within its normal bandwidth of operation. The technique may be employed in various resonator structures, including a ring resonator.

Abstract: An electron beam and a positron beam are separately accelerated and stored to a predetermined energy, both beams are joined (in a predetermined direction), and a free positronium beam is generated. As a result, on the positronium beam axis, a monochromatic gamma ray having an energy twice the electron energy and a monochromatic X-ray having a photon energy of 1.3/10.sup.6 of this gamma ray are generated as irradiation light.

Abstract: An approach is shown for eliminating the expense of a plurality of linear accelerators as used in a multiple electron beams free electron laser system. A single linear accelerator is used to simultaneously accelerate a plurality of electron beams by using an electron beam deflection means such as a bending magnet to cause multiple beams to converge to a single stream of electrons for acceleration by the linear accelerator and then using a similar beam deflection means to re-define the accelerated beams in accordance with their repsective enery levels into a similar plurality of output beams.

Abstract: This invention relates to a high-performance gyrotron for the production of electromagnetic millimeter or submillimeter waves with a quasi-optical resonator. The latter is formed by two concave mirrors (1, 2) placed mutually opposite one another on an optical axis. For increasing the decoupling efficiency as well as for reducing the radiation into the environment the quasi-optical resonator is placed in a housing (4), which at least in sections is electrically conductive.

Abstract: Feedback oscillations in a free electron laser are suppressed without significantly degrading the laser performance by means of an attenuator placed in a linear gain zone of its interaction region.

Abstract: An FEL array is comprised of adjacent FEL modules. Each module preferably uses a ribbon beam plasma-anode E-gun (PAG) or another plasma-assisted E-gun to produce a planar E-beam that interacts with a planar wiggler magnetic field. The modules may share a common electron gun. A control signal is input through a phase priming array to preselect the radiation mode. A planar, distributed Bragg resonator/reflector is used to set up a high-Q cavity, enabling the low gain module to produce high power radiation. The FEL modules are arranged in an array to reduce the output radiation flux density while achieving high output power density in the far-field, and to permit beam steering by phase control of individual modules. The relatively low current density of the individual E-guns lessens the size of the guiding magnetic field in each module to the extent that the wiggler magnetic field alone is sufficient to perform this guiding function.

Abstract: A free-electron laser has a wiggler for a linear electron beam comprising two sets of magnetic polepieces 26, 28 periodically spaced along opposite sides of the beam. The polepieces of one set 28 are displaced along the beam from the other set 26 by one-half period. A uniform longitudinal magnetomotive force generates fields between polepieces having transverse components 22 alternating between the sets 26, 28, providing a very short periodicity and hence, high frequency wave radiation.

Abstract: A static periodic field device for a free electron laser has a plurality of holes therethrough to allow the interaction of electrons flowing therethrough to interact with either an electric or a magnetic fields as desired. The device is composed of a plurality of conducting layers separated by insulating layers and appropriately connected to provide either an electric or a magnetic field therein. The separation of the conducting layers determines the raidated energy wavelength.

Abstract: A laser arrangement includes electron beam apparatus comprising a plurality of electrodes, each of which having an aperture therethrough. The apertures are aligned along the longitudinal axis of an envelope which surrounds them and contains gas. The electrodes are electrically connected such that, of an adjacent pair, one is at a lower potential than the other. An electron beam is produced between the first electrode and an adjacent electrode, and is accelerated along the axis through the apertures, the electron current increasing in magnitude. The electron beam produced is used to provide pumping powder to the gas contained within the envelope such that it acts as a laser amplifying medium.

Abstract: In an FEL, unwanted sidebands in the laser pulses are suppressed by the introducing of a temporal dispersion of the sideband with respect to the main wavelength, causing a time lag between the main wavelength and the sideband. This is preferably accomplished by the use of diffraction gratings in a grating rhomb within a ring resonator. The first of the gratings in the rhomb has a zero order diffraction which can be used for outcoupling. Tuning in real time is achieved by adjusting the positions of the elements in the ring resonator so that the desired wavelength will be in spatial overlap with the electron pulses in the wiggler.

Abstract: An orotron for generating near millimeter wavelength radiation at a selectable output frequency within a wide frequency range, in which the orotron output power is automatically tuned electronically at the selected output frequency. A piezoelectric electromechanical positioning device is connected between the two mirrors forming the open resonator of the orotron to determine the mirror separation in accordance with a position control signal. The electron beam acceleration voltage, which determines the orotron output frequency, and the position control signal are adjusted simultaneously so as to tune the output power at a single oscillation mode of the orotron resonator over a wide frequency range. In the preferred embodiment, the actual output frequency is detected and compared with the selected output frequency, and the beam acceleration voltage and mirror separation simultaneously adjusted to continuously tune and maintain the orotron output at the selected frequency.

Abstract: A free electron laser (FEL) is described which is used for generating high ower radiation in a region of increasing guiding magnetic field before injection into an undulating low magnetic field. It includes an electron beam propagating along a guiding magnetic field B.sub.0 (approximately 10 kilo gauss) inside a hollow metallic tube used as a wave guide. Around the path of the beam, an undulator in the form of a bifilar helical winding or the like produces a periodic magnetic field B.sub.1 (approximately 0.5 to 1.0 kG). The electron motion accordingly has a substantial transverse component and the motion at the cyclotron and undulator frequencies occurs. Due to the energy exchange between the gyrating component of electron motion and an electromagnetic wave already present in the hollow tube, radiation of a calculable frequency is amplified.

Abstract: A free electron laser (FEL) is disclosed in which the phase of the output electromagnetic beam is inherently adjustable without the use of any extraneous optical phase shifting materials. This is accomplished by implementing the FEL as a pair of series-connected wiggler cavity sections, and varying the relative phases of the bunched electron flow in the first cavity section relative to the second. In a preferred embodiment a series of electrodes are provided in a transition region between the two cavity sections, and variable voltages are applied to the electrodes to electrostatically control the electron transit time through the transition region, and the electron velocity upon exiting from that region. This translates into a control over phase and frequency.

Abstract: A free-electron laser capable of operation at a shorter wavelength than the fundamental lasing wavelength, but without any increase in electron energy requirements. The laser includes a conventional high-energy electron beam source and a wiggler transverse magnetic field through which the beam is passed to produce lasing. Opposed optical mirrors are selected to be reflective at a selected harmonic wavelength as well as at the fundamental wavelength. Lasing is initiated at the fundamental wavelength, but is then supported at the selected harmonic wavelength as well. By appropriate design lasing at the fundamental wavelength may be subsequently terminated without affecting lasing at the harmonic wavelength, which continues at a substantially reduced energy cost than would have been incurred if lasing at the harmonic frequency been initiated in a fundamental mode.

Abstract: In gyrotron devices, pitch factor and efficiency are directly proportional. When the pitch factor is increased, however, a larger starting current is needed. The available power supply thus limits the pitch factor and subsequently, the efficiency of the device. The present invention is a gyrotron device in which the pitch factor is adjustable. When starting the gyrotron the pitch factor is set to a low level and only a small starting current is required. After the device has been started, the pitch factor can be increased to increase the oscillation efficiency.

Abstract: A free electron laser for use with a short-pulse relativistic electron source. The device includes a resonant optical cavity in which a spatially-periodic magnetic field is produced by a wiggle magnet assembly. An input optical beam having a wavelength lying within the gate bandwidth of the free electron laser interaction is injected into the cavity. A beam of relativistic electrons produced by a short-pulse source, such as an RF-linac, is injected into the cavity. The electron beam and the input optical beam interact under the influence of the magnetic field to amplify the input optical beam.

Abstract: In a method and apparatus for amplifying and/or generating electromagnetic wave radiation, a gas plasma region having a non-Maxwellian electron distribution is produced by effecting collisions between scattering particles in the gas with free electrons which have been accelerated to an energy level which is greater than that providing maximum probability of collision of the electrons with scattering particles in said gas; and the electromagnetic wave radiation is subjected to the plasma region such as to produce amplification of the radiation by stimulated emission of Bremstrahlung from scattered free electrons in the plasma region.

Abstract: A radio frequency linear acceleration free electron laser is provided by ing the pulses in such a time delay manner to phase lock the device and produce phase correlation between the laser pulses.

Abstract: Apparatus and a related method for controlling the characteristics of a high-power laser beam to provide a desired beam divergence, spectral content, and phase. A high-power beam, as from a free-electron laser, is directed into a conical Raman amplifier, together with a Stokes seed beam having the desired characteristics. The amplified output from the amplifier is divergent and its intensity falls of rapidly enough to allow the use of solid material optics without damage or destruction of the optical elements. The Raman amplifier is contained in part by two moving-gas windows, which seal the amplifier from the vacuum environment of the laser without the use of solid material optics. In one embodiment of the apparatus, the resulting output beam is precorrected for phase aberrations caused by optical elements and the transmission medium through which the beam is directed.

Abstract: The invention envisages control devices acting on the laser to vary in time the electron/photon interaction, means proceeding to a State I in which they alter the optimal conditions for laser amplification; and a State II in which that reestablish said optimal conditions, which control devices permit the improvement of the peak amplitude and stability of the laser pulses and the rate and stability of the pulse period. According to another aspect of this invention, the two states are alternated, preferably periodically or almost periodically. The duration of State I should be selected by comparison with the characteristics of the electron packet and, in particular of the relaxation time observed for said packet. If the duration of State II is set to a value to be comparable to or longer than the electron relaxation time, the peak amplitude of the laser pulses is increased. The duration of State II should be selected by comparison with the natural macropulse width.

Abstract: An improved radiation source is disclosed, exploiting the spontaneous radiation generated from the interaction of an electron beam and a conductive grating. Conditions are defined for generating coherent or noncoherent radiation, and for extending the tunability of the radiation source from millimeter, IR, visible and UV wavelengths to x-ray wavelengths, and for generating multiple wavelengths simultaneously. Conditions are disclosed for enhancing the intensity of the spontaneous radiation, anf for modulating the radiation.

Abstract: Free electron laser apparatus that provides a magnetic centering force to turn or focus a non-axial electron toward the longitudinal axis as desired. The focusing effect is provided by wiggler magnet pole faces that are approximately parabolically shaped.

Abstract: A self-aligning, high-power, free electron laser (FEL) oscillator 10, comprises a self-aligning feedback, element 12 located near the electron beam input end 14 l of the FEL wiggler 16; a partially transmitting stimulated Brillouin scattering (SBS) plasma mirror 18 located near the output end 20 of the laser wiggler 16; and a plurality of laser beam expansion elements 32-32.sup.n located in succession on the path of the resulting output laser beam 34 for magnifying the output laser beam 34 to a desired output diameter. A totally reflecting, removable start-up mirror 30 is located between SBS plasma mirror 18 and laser beam expansion elements 32-32.sup.n. The removable start-up mirror 30 provides feedback until the SBS threshold is reached.

Abstract: An optically pulsed electron accelerator can be used as an injector for a free electron laser and comprises a pulsed light source, such as a laser, for providing discrete incident light pulses. A photoemissive electron source emits electron bursts having the same duration as the incident light pulses when impinged upon by same. The photoemissive electron source is located on an inside wall of a radio frequency powered accelerator cell which accelerates the electron burst emitted by the photoemissive electron source.

Abstract: An apparatus and method for enhancing the efficiency of a free electron laser, (10). A plurality of electrodes, (28) are imbedded in an electrically insulating vacuum tube, (18) enclosing the electron beam, (14) and its copropagating electromagnetic wave. A variable computer controlled high voltage d.c. power supply, (29) is connected to the electrodes, (28) for energizing the electrodes, (28) at saturation indicated by detectors, (30) thereby converting d.c. electric potential to electromagnetic radiation without gain degradation.

Abstract: A blazed corrugated reflector having internal corrugations or vanes, blazed at specified design angles, coherently reflects power at specified wavelengths. The corrugations meet the criteria of effecting retroreflection according to the Bragg conditions for gratings, eliminating higher order modes of reflection, and maximizing retroreflection and minimizing forward scattering according to the blaze condition. Two such reflectors can be configured into a laser resonator by placing them at opposing ends of a matching waveguide. The reflector does not obstruct the passage of an axial electron beam, thereby making it suitable to implement the resonator portion of a free electron laser.

Abstract: An ion or electron beam is steered or focussed by a circular magnetic field produced by passing a large electrical current through a straight conducting wire, the magnetic field being co-axial with the wire. Annular beams of charged particles coaxial with the straight wire can be focussed onto a circular spot or, depending upon the entry radius of the annular beam and the magnetic field strength, can be induced to follow a looping trajectory. The effect of the steering or focussing system can be enhanced by the provision of a cylindrical conductor which is co-axial with the straight conducting wire and maintained at a voltage sufficient to produce the desired particle trajectory such that the particle beam passes between the wire and the cylindrical conductor. The beam steering or focussing systems is applicable to the fields of beam current density intensification, ion implantation, ion separation and free electron lasers.

Abstract: A method of cooling an electron beam with electrons having energies in excess of 10 MeV by directing a cooling laser beam over the path of the electron beam so as to achieve Compton scattering interactions, and a device which utilizes this method with other elements to produce a free electron laser system having much greater efficiencies than a single pass free electron laser.

Abstract: A source of coherent radiation. The source includes an evacuated drift tube having an input end for receiving a beam of relativistic electrons and an output end for providing coherent radiation. A relativistic electron supply provides the beam of electrons to the drift tube input end, and a magnetic field is provided for causing the relativistic electrons to spiral. An azimuthal wiggler causes the spiraling electrons to undergo accelerations while an axial magnetic field is provided for controlling the gyroradii of the spiraling electrons acted upon by the wiggler.

Abstract: An ion or electron beam is steered or focussed by a circular magnetic field produced by passing a large electrical current through a straight conducting wire, the magnetic field being co-axial with the wire. Annular beams of charged particles coaxial with the straight wire can be focussed onto a circular spot or, depending upon the entry radius of the annular beam and the magnetic field strength, can be induced to follow a looping trajectory. The effect of the steering or focussing system can be enhanced by the provision of a cylindrical conductor which is co-axial with the straight conducting wire such that the particle beam passes between the wire and the cylindrical conductor. The beam steering or focussing systems is applicable to the fields of beam current density intensification, ion implantation, ion separation and free electron lasers.

Abstract: Free-electron lasers and masers are modified by eliminating the resonator cavity as such. The feedback mechanism, essential to oscillation, is distributed through and integrated with the transmission line which guides the electromagnetic wave at the active region where interaction with the electron beam takes place. The feedback structure is created by perturbations in the transmission line along the length thereof at the locations of the zero electric field lines of a desired oscillatory standing wave mode. The perturbations may take the form of axial, helical, and azimuthal deformation of the transmission line.

Abstract: A free electron laser for emitting coherent radiation. The laser includes a wiggler magnet for producing a spatially periodic magnetic field in a drift region into which relativistic electrons are injected in a predetermined direction. An axial magnet is provided which generates an axial magnetic field parallel to the above predetermined direction. The axial field is tapered in field strength within a uniform wiggler region, wherein the wiggler field is of uniform and constant magnitude, such that the tapered field acts to oppose the change in axial electron velocity resulting from the free electron laser interaction as electrons travel through the drift region. The tapered axial field acts to enhance power output and efficiency.

Abstract: This transformer (9) is formed by a waveguide, of approximately elliptical cross-section, and with increasing eccentricity (e) along the axis (z) of the transformer. This transformer (9) is connected on one side to the cavity (1) of a gyrotron (11) and on the other side to a section of guide (13) having the same cross-section as the final cross-section of the transformer and of which the cross-section is constant along the axis (z) of the transformer.The transformer receives from the gyrotron cavity a complex mode, of TE.sub.on type, and changes said mode into a mode in which the electrical field is approximately parallel to a given direction (z). A system of two mirrors (M.sub.3 and M.sub.4) enables a single beam of plane waves (19) to be obtained from the two beams of plane waves (14 and 15) obtained at the output of the section of waveguide (13).

Abstract: A gyrotron device comprising a magnetron injection gun for emitting a sectionally-ring-shaped electron beam, a superconducting coil for applying magnetic field to the electron beam emitted from the gun, a ring-shaped resonator mirror for quasi-optically reflecting and resonating those electromagnetic waves which are oscillated when the electron beam passes along the magnetic lines of force generated by the superconducting coil and which propagate in the radial direction, while radially emitting a portion of the electromagnetic waves, and a plurality of transmission mirrors for quasi-optically reflecting and transmitting the electromagnetic waves which have been emitted in the radial direction of the resonator mirror.

Abstract: A device for converting the kinetic energy of an intense relativistic electron beam (IREB) into trains of multi-gigawatt AC electrical pulses comprising a foilless diode for generating an IREB and injecting the IREB into one end of a drift tube. The device further includes a modulating circuit for modulating the IREB current while in the drift tube to obtain longitudinally spaced bunches of electrons, and a coaxial transmission line with the end of its center conductor disposed across the other end of the drift tube in the path of the IREB. A gap is disposed between the end of the drift tube and the end of the center conductor. The modulated IREB induces a voltage in the coaxial transmission line. This voltage appears across the gap to slow down the electrons and to convert the kinetic energy of the IREB into electrical energy that propagates along the coaxial transmission line.

Abstract: A collective interactive klystron that utilizes a bent drift tube to achi circular motions of the electrons in the drift region. This bent drift tube eliminates material repulsion between AC space charges in a klystron.

Abstract: A cyclotron resonance maser system includes coaxial coupling between coaxial wave guides. Such coupling is provided between an outer coaxial waveguide through which a gyrotron electron beam passes in generating or amplifying microwaves and an inner coaxial waveguide terminating in an annular window. The coupling separates the microwaves from the electron beam before the collector region of the gyrotron so that the collector dimensions are not related to, and hence restricted by, the wavelength of the output microwaves. The particular preferred coupling includes substantially axial slots in the common wall between the respective waveguides which slots provide selective coupling between the waveguides in the desired modes and limiting mode conversion. The coupling is preferably between a TE.sub.On or TE.sub.ml mode in the outer input waveguide and a TE.sub.On' mode in the inner, output waveguide, n and n' being integers greater than 1. A preferred resonant cavity limits the generated microwaves to a TE.sub.

Abstract: A free electron laser in which the electron beam 12 is sent through the field of a quadrupole magnet 16 which may be untapered or tapered. The beam 12 is sent through the magnet 16 spaced from the symmetry axis of the magnet's poles 22 but on the focusing plane 20 of the quadrupole magnet 16.

Abstract: Method and apparatus for modulating coherent radiation generated by an orotron in accordance with a low voltage control signal applied to the diffraction grating to vary the grating-to-cathode voltage from the cathode-to-collector voltage over a selected voltage range determined by the maximum and minimum values of the control voltage. For amplitude modulation, the grating-to-cathode voltage is varied within a voltage range between a lower voltage at which the orotron output power starts to fall abruptly and a cutoff voltage at which coherent radiation ceases. For frequency modulation, the grating-to-cathode voltage is varied within a voltage range, including the point of maximum power output, where there is a minimum change of output power with a change in the grating-to-cathode voltage.

Abstract: A method and apparatus for increasing the power output and efficiency of an orotron generating near millimeter wavelength radiation. In accordance with a theory of orotron operation described herein and confirmed experimentally, the ribbon-like electron beam utilized in the orotron has a very high current density to effect a large increase in orotron output power and efficiency due to space-charge effects in the beam. In the preferred embodiment, the high density electron beam is generated by a closely-packed rectangular array of field-emission cathodes.

Abstract: An electron beam device which includes a vacuum enclosure which houses an electron gun for producing an annular beam of helically rotating electrons, an iris-loaded waveguide which is supplied with high frequency power and serves to create a high frequency electromagnetic field along the axis of the beam which has a longitudinal electric field component along the beam axis, and a resonator which abstracts high frequency energy from the beam. A coil surrounds the vacuum enclosure to provide a magnetic field of increasing strength with distance downstream in the region of the iris-loaded waveguards whereby the angular velocity of the electrons in the beam is increased with little change in the axial velocity.

Abstract: A technique for accelerating charged particles using an intense traveling electromagnetic wave such as produced by appropriate wavelength lasers. Low energy electrons injected into the focal region of an intense, polarized laser beam are rapidly accelerated in the direction of the beam by the ponderomotive force of the radiation field. The particles reach maximum energy in a distance comparable to the Rayleigh range of a tightly focussed, visible wavelength, diffraction limited pulsed laser. At this point, a combination of induced transverse velocity drifts and/or the rapidly decreasing electric field strengths due to the expanding laser beam envelope cause the particles to enter a low radiation field region before significant deceleration can occur. The resulting device possesses unique advantages and properties not present in existing accelerators.

Abstract: A tilt-angle electron gun provides a conical beam of electrons for injection into an axially aligned magnetic field of a gyrotron tube. The beam is formed by an electrostatic lens system for focussing and accelerating the electrons within a magnetically shielded region. The conical beam is substantially monoenergetic and laminar so that after injection into the magnetic field the resulting hollow beam has gyrating electrons which have an axial velocity spread sufficiently low for high efficiency gyrotron amplification.

Abstract: A method and apparatus for suppressing lower order cyclotron harmonics in order to permit resonance within a quasi-optical gyrotron/gyroklystron configuration of a desired higher order harmonic. In the gyrotron/gyroklystron configuration at least one open resonator defined by at least two mirrors is positioned downstream from an electron beam source for receiving therethrough the beam of electrons and for exchanging energy therewith. This method includes the steps of choosing a mirror radius size .rho. for the mirrors forming the at least one open resonator which is large enough relative to the spot size of a desired radiation cyclotron harmonic .omega..sub.n so that the harmonic .omega..sub.n oscillates within the at least one resonator, but small enough so that the spot size for the next lower cyclotron harmonic .omega..sub.m is larger than the mirror so that the harmonic .omega..sub.m does not oscillate due to diffraction losses.