US3363138A - Electron beam-plasma device operating at multiple harmonics of beam cyclotron frequency - Google Patents

Description

Jan. 9, 1968 s. GRUBER ET AL 3,363,138

ELECTRON BEAM-PLASMA DEVICE OPERATING AT MULTIPLE HARMONICS OF BEAM CYCLOTRON FREQUENCY Filed Nov. 4, 1964 4 Sheets-Sheet 1 ZM B BY PETE/1 L. AUEI? QAJ=1M ATTORNEY Jan. 9, 1968 s. GRUBER ET AL 3,363,138

ELECTRON BEAM-PLASMA DEVICE OPERATING AT MULTIPLE HARMONICS OF BEAM CYCLOTRON FREQUENCY SHELDON GRUBEE PETER L. AUEI? BY 90L #1 b 2 ATTORNEY Jan. 9, 1968 s. GRUBER ET AL 3,3

ELECTRON BEAM-PLASMA DEVICE OPERATING AT MULTIPLE HARMONICS. OF BEAM CYCLOTRON FREQUENCY 4 Sheets-Sheet 5 Filed Nov. 4, 1964 INVENTORS SHELDON GRUB/57'? PETE/P L. AUER ATTORNEY Jan. 9, 1968 s. GRUBER ET AL 3,363,138

ELECTRON BEAM-PLASMA DEVICE OPERATING AT MULTIPLE HARMONICS OF BEAM CYCLOTRON FREQUENCY Filed Nov. 4, 1964 4 Sheets-Sheet 4 INVENTORS SHEA DO/V GRUB/5R P5755 L. [II/ER A TTO/ P/VEY United States Patent 3,363,138 ELECTRON BEAM-PLASMA DEVICE OPERA'HNG AT MULTIPLE HARMONICS 0F BEAM CYCLO- TRON FREQUENCY 5 Sheldon Gruber, Sudbury, Mass, and Peter L. Auer,

Chevy Chase, Md., assignors to Sperry Rand Corporation, Great Neck, N.Y., a corporation of Delaware Filed Nov. 4, 1964, Ser. No. 409,003

9 Claims. (Cl. 315-39) 10 ABSTRACT OF THE DISCLOSURE of the plasma cyclotron frequency.

This invention relates to electron stream apparatus for generating and amplifying electromagnetic waves, and more particularly to such devices capable of reliably operating at frequencies much higher than the frequencies at which currently known electron stream devices operate.

There is at present a considerable effort being devoted to develop efficient and relatively simple devices for generating and amplifying electric field waves in the higher ranges of the microwave frequency spectrum, and in the millimeter and submillimeter wavelength ranges. Conventional oscillators and amplifiers such as the diverse types of magnetrons, klystrons and electron beam-traveling wave interaction devices have physical dimensions that are of the order of wavelengths of the waves that they generate or amplify. At very high frequencies these devices are so small in size that they are extremely diflicult to manufacture, are costly, and the power of the waves that they can generate and amplify is quite low. Some consideration has been given to the generation and amplification of electromagnetic waves by the use of devices that employ a stream of electrons that passes through an ionized gas, i.e., a plasma. It was hoped that in this way the limitations on size and tolerances of dimensions could be avoided. It has been found by most investigators, however, that in order for the beam-plasma devices to function in a practically useful way, the plasma density must be high, and therefore so must be the strength of the magnetic field that confines the plasma and the electron beam. This rer quires large, heavy, and expensive magnets. Furthermore, the axial phase velocities of the interacting beam and plasma waves are low so that special slow wave propagatmg circuits, and associated coupling means, must be provided. 59

In most prior investigative work involving electron stream and electric field Wave interactions in a gas plasma, and in the presence of a steady axial magnetic field, it was assumed that beam electrons had only axially directed velocities and the conventional negative-energy slow space charge beam wave or the slow fundamental cyclotron wave interacted with a plasma Wave that fell within one of the two propagating bands of the plasma, i.e., one frequency band being from 0 to w ore whichever was the smaller, and the second hand being from the larger of w or u to (w -i-w where w is the radian cyclotron frequency and is equal to e/ m B, and u is the plasma radian plasma frequency and is equal to where e/m is the charge to mass ratio of an electron, B is the axial D.C. magnetic field strength, n is the plasma electron density, and s is the dielectric constant of free space.

In devices whose operations depend upon interactions of the types just described, it is apparent that the maximum possible frequency of operation is in the frequency ange (w +w and because this frequency is a function of the plasma electron density n and the axial magnetic field strength B, it is impractical, in terms of apparatus'to generate or amplify waves much above a frequency of several gigacycles (cycles x10 Some investigators have reported observing radiations in the frequecy range of multiple harmonics of the cyclotron frequency from beam-plasma devices, but to date they have been little more than laboratory curiosities and no satisfactory explanation has been offered for them.

It therefore is an object of this invention to provide wave-propagating electron stream apparatus for generating and amplifying electric field waves at, and above, the higher microwave frequencies.

Another object of this invention is to operate a magnetically-focussed electron beam device in such a manner that the electrons of the beam have sufiicient velocity in the direction transverse to the beam axis to give rise to negative energy transverse electrostatic beam waves in the regions of integral multiples of the beam cyclotron frequency, these waves coupling to and amplifying transverse electrostatic plasma waves at comparable frequencies and phase velocities.

A further object of this invention is to provide an electron bearn-electric field interaction device in which one of the interacting waves is an electrostatic beam wave at a frequency near an integral multiple of the beam cyclotron frequency and which has a high phase velocity in a direction parallel to the beam axis.

In accordance with one embodiment of the present invention, means are provided for producing an electron beam that flows along an axis through a gas plasma. A unidirectional magnetic field is directed along the axis and confines the electron beampAn essential characteristic of the beam is that the electrons must have a large component of velocity in a direction transverse to the beam axis, the electrons thereby executing a spiraling motion about magnetic field lines as they move axially along the beam. Under these conditions there exists on the beam a family of high frequency transverse electrostatic waves having respective positive energy and negative energy waves in the vicinity of each higher harmonic of the cyclotron frequency. The plasma electrons also must have large rotational energies about the magnetic field lines so that the plasma supports a family of high frequency transverse electrostatic waves which also fall in the vicinity of the higher cyclotron frequency harmonics. The signal to be amplified is at a frequency in the vicinity of one of the higher harmonics of the cyclotron frequency and is coupled to electrostatic waves in the plasma at a corresponding frequency and having a phase velocity that is substantially synchronous with that of the beam Waves. Certain parameters of the beams and plasma are judiciously proportioned to assure stable propagation of the respective Waves. Interaction takes place between the beam and plasma waves with the negative energy beam wave giving up energy to the plasma wave and thereby amplifying it. Means are provided for coupling the amplified wave from the plasma. The interacting waves in the beam-plasma system are characterized by having a high axial phase velocity much higher than the axial velocity of the beam so that the input and output coupling means may be higher phase velocity circuits and transmission lines, thus obviating the need for special slow wave circuits and coupliug means as conventionally required in present day elec- V tron beam-wave interaction devices.

The present invention will be described in connection with the accompanying drawings wherein:

FIG. 1 is a simplified sketch illustrating the type of electron motion that is required in the beam employed in devices operating in accordance with the present invention;

FIG. 2 is a graph of the plasma dispersion function Z which appears in the equation for the dielectric constant of a beam and a plasma;

FIGS. 3 and 4 are dispersion curves of the beam and plasma, respectively, which are proportioned in accordance with the teachings of this invention; and

FIGS. 5, 6 and 7 are simplified illustrations of three diiferent beam-plasma devices that are constructed to operate in accordance with the teaching of the present invention.

Before proceeding with a detailed description of the apparatus for carrying out the invention, it is believed that it will be helpful to first presentan explanation of the characteristics and critical features of the beam and plasma which give rise to the generation and amplification of the transverse electrostatic waves at frequencies in the regions near multiple harmonics of the beam cyclotron frequency. An essential feature for devices operating in accordance with this invention is that the electrons of the beam which traverse the plasma must have substantial speeds in a direction transverse to the axially directed steady magnetic focussing'field B. It further is assumed that the axial electrostatic space charge fields are neutralized by the ions of the plasma that surrounds the beams. The beam electrons execute a spiraling motion about the axially directed steady magnetic field lines, as represented quite generally in FIG. 1, wherein the encircled crosses represent magnetic field lines directed into the plane of the paper and the spiraling electrons are represented by dots on a respective orbit. The spiraling electrons give rise to transverse electrostatic waves having short transverse wavelengths as illustrated for two of the electrons in FIG. 1, these transverse electrostatic waves being of importance in the 7 understanding of the present explanation. The character of these waves may be explored by investigating the electrostatic dispersion equation for the beam, this being derived from the equation of the longitudinal dielectric constant of the beam. The equation for the longitudinal dielectric constant of a beam is known and may be written k being defined as 27/), A being wavelength, I is the Bessel function of argument 11 is an integer, and

. 4 g V is the velocity distribution function of the beam electrons. Considering that the beam electrons have a spread in axial and perpendicular velocity as a result of the cathode temperature as well as the spread introduced by the generation of the perpendicular electron motion, the velocity distribution function of the beam, assumed to be Gaussian or Maxwellian, may be given as 2 hen? where k u, and (n) is the plasma dispersion function and maybe defined in general terms as equal to is the modified Bessel function of the first kind of imaginaryargument, the argument A being defined as The plasma dispersion function Z03 and the term 5,, are extensively defined and evaluated in the book The Plasma Dispersion Function, by B. D. Fried and S. D.

Conte, published by Academic Press, New York and London, copyright 1961. The variable i has both real and imaginary parts, i.e., =x+jy, and has the significance of the ratio of phase velocity of a wave to some thermal velocity. The existence of the imaginary part of g indi-' cates that the dispersion relationship, presently to be derived, will exhibit wave damping, the damping for n=0- being known as Landau damping while the wave damping for frequencies in the neighborhood of a cyclotron har-'' monic frequency mu is known as collisionless cyclotron damping. The real and imaginary parts of Z are plotted in FIG. 2.

It may be seen in FIG. 2 that for values of around 1.4 i.e. /2, the magnitude of the imaginary part that gives riseto wave damping becomes quite small. Therefore,

evaluating the equation for the dielectric constant with" the condition 5,,1, and assumingvpnt Equation 3 be- 5. Setting Equation equal to zero gives the dispersion equation for a low density beam (w w as approximately 3: gf (a-mw,Xa-mw.w I (x)x@, 1. (mw w (7\)e 5Jmw fiknu is approximately satisfied.

The minimum ratio of transverse to longitudinal beam electron velocities to assure that relatively undamped transverse electrostatic waves will propagate on the beam may be estimated by substituting the quantity [c m for (:)mw

in Equation 6. For the mth mode, and using fiim' as the maximum value of I (7\)e (which occurs when the minimum ratio may be expressed as Now considering further the beam wave dispersion curves of FIG. 3, it is seen that the beam will propagate two undamped waves in the neighborhood of each cyclotron harmonic frequency. By applying an extension of the well known Chu kinetic power theorem it can be shown that the upper frequency curve, ai mw of each pair carries positive energy and the lower frequency curve,

z mw of each pair carries negative energy. Should the negative energy beam wave couple to a positive energy beam wave, the positive energy wave will grow in amplitude due to energy transfer from the negative energy wave, and the beam itself will become unstable. For devices intended for use as oscillators this would be required, but for a device intended for use as an amplifier of an applied external signal, this condition must be avoided. At sufficiently high electron densities in, the positive energy wave for the mth mode will intersect the negative energy wave of the m+1th mode, thereby giving rise to the aforedescribed beam instability. The critical or maximum electron beam density which will avoid these instabilities may be estimated by setting the asymptotes for the negative energy wave at the m+1th cyclotron harmonic equal to the positive energy wave at the mth cyclotron harmonic, which for the beam described in Equation 2 is An approximate evaluation for Equation 9 is Having thus shown that a beam whose electrons have significant transverse velocity v will stably propagate transverse electrostatic waves at frequencies in the region 5% as v =u and w=0. Because the dielectric constant equation for the gas plasma also includes the plasma dispersion function Z of Equation 4, the relationship e u t must again hold true in order to avoid collisionless wave damping in the warm gas plasma. With these basic relationships defined, the longitudinal dielectric constant of the warm plasma may be expressed as 2 -xiiL n= m 11) where w is the radian plasma frequency of the warm plasma and all other quantities in the expression have the same definitions as given above, except that here they now refer to the warm plasma rather than the beam. Equation 11 is solved for frequencies in the neighborhood of w=mw, by removal of the m-th term and evaluating all the other terms at w=mw with the assumption that thereby giving the following for the dispersion relationship of the warm gas plasma:

FIG. 4 is a plot of Equation 12 for several different values of w /w and for a limited range of w/w The curves of FIG. 4 show generally that the frequencies of the plasma waves may be on either side of the harmonics. The plasma electron densities, i.e., u that give upper hybrid solutions between any two harmonics form the boundaries between two density regions. At higher plasma densities the curves approach the higher harmonics as A approaches zero. At lower densities they approach the lower harmonics. All the curves have the common feature that they approach the cyclotron harmonics on the high frequency side at large values of A. The curves of FIG. 4 are positive energy curves.

It may be seen from the above explanation that both the electron beam and the warm plasma will support transverse electrostatic waves at high frequencies in the ranges of multiple harmonics of the cyclotron frequency. Therefore, by proportioning the parameters of the beam and the warm plasma in accordance with the above teachings it is possible to produce a negative energy beam wave and a positive energy plasma wave which have substantially the same phase velocities at a selected frequency in a region of a multiple cyclotron harmonic frequency, there by providing the necessary conditions that are required for amplification of an applied signal at the selected frequency. In amplifying devices operating in this manner, input coupling means are provided for coupling electromagnetic waves at the selected frequency to the positive energy electrostatic plasma waves, and similarly, output coupling means are provided for coupling the amplified electrostatic waves to external wave propagating means in which the waves propagate as electromagnetic waves.

Although the above development of the transverse electrostatic beam waves assumed that the beam electrons had a Maxwellian velocity distribution function, it will be understood that in an actual beam of the type under consideration, this assumption will not be strictly true. However, the departure in practice from this assumption actually will be more favorable to the generation of the transverse electrostatic waves with which this invention is concerned.

FIG. 5 is a simplified illustration of a beam-plasma device that functions as an amplifier in accordance with the principals explained above. As emphasized in the above discussion, it is a necessary requirement that the beam electrons have high speeds in a direction transverse 7 to the beam axis, and in the embodiment of the invention illustrated in FIG. this is accomplished by the use of a shielded electron gun 10 which produces a beam of electrons which enters the longitudinally directed magnetic focussing field at a region where the magnetic field lines have radially directed components, thereby'imparting a spiraling motion to the electrons. Electron gun 10 may be of the type described in US. Patent 2,707,758, issued May 3, 1955 to C. C. Wang and assigned to applicants assignee. The gun is comprised of an electron emissive surface 11 and an accelerating anode 12 which produces a confined stream of electrons which traverses the length of a vacuum tight cylinder 14 and which is terminated in collector electrode 15. Cylinder 17 and an annular member 18, both of magnetic material, shield the gun from the magnetic focusing field which is produced by a longituvdinally'extending electromagnet 20. Annular member 18 serves as a pole piece to cause the lines of magnetic flux to curve radially outwardly in the region where the beam enters the magnetic field, thereby producing the radial components of magnetic field which impart the transverse component of velocity to the beam electrons. Annular members 21 and 22 are disposed at each end of electromagnet 20 to complete the magnetic circuit.

. Cylinder 14 is made of a low loss dielectric material such as glass or quartz and is provided with a port 25 through which an ionizable gas such as cesium, for example, may be admitted, the port then being pinched off when adesired gas pressure, has been achieved within the interior of the device. 7 V

Disposed about the dielectric cylinder 14 is an input resonant cavity 27 and an output'resonant cavity 28. Cylinders of conductive material 30, 31 and 32 surround the dielectric cylinder 14 in the regions at the ends of cavities 28 and 29 and in the region therebeween so as to provide a conductive boundary about the cylinder 14. Signals to be amplified at a frequency near a multiple harmonic frequency are coupled through the'coaxial coupler 33 into the'input cavity 27, and after amplification are coupled 7 from output cavity 28 by a similar coaxial coupler 34. 7

Because the beam waves and the plasma waves with which we are concerned are electrostatic waves whose electric fields extend transversely to the beam axis, resonant cavities 27 and 28 must resonate in a mode which also has transverse electric fields in order that the input and output electromagnetic waves may couple to'and from the desired electrostatic waves of the beam. and plasma. As an example, resonant cavities 27 and 38 may resonate in the TE mode, although any TE mode should be satisfactory.

As pointed out in the above development, certain critical parameters must be established in the beam and in the plasma in order that'the stable transverse electrostatic waves may propagate on the beam and plasma. For example, the temperature of cathode 11, the potential of accelerating anode 12, and the strength of the magnetic focusing field B provided by electromagnet 20 are proportioned so that the relationships expressed in Equations 7, 8 and 10 are satisfied for the electron beam. Similarly,

with regard to the warm gas plasma, the relationshipsof the magnetic field source. Another important advantage arising in devices operated in accordance with the present invention is that the axial wave number k of the beam and plasma waves must be relatively small in order to avoid collisionless Wave damping, as explained in connection with the discussion of the plasma dispersion function Z (5). Since the axial wave number k is inversely related to the axial phase velocity 11 of the waves, this means that the phase velocity of the waves that enter into coupling relationship must be very high, and in practice this velocity is higher than the beam drift velocity v This then means that slow wave propagating circuits are not necessary to couple the waves into or out of the plasma-beam system nor are they necessary in the interaction region of the device. Consequently, conventional electromagnetic wave transmission lines having high phase velocities may be employed throughout, thereby simplifying the design and the manufacture of the devices.

In the above embodiment of the invention it is contemplated that the gas contained within dielectric cylinder 14 will be ionized due to the collision of the beam electrons with the atoms or moleculesof the ionizable gas that is employed. Although this method for. generating plasma is presently preferred because of its simplicity, it should be understood that other methods for generating the plasma may also beemployed, if so desired. For example, the plasma may be generated by means of a separate are or spark discharge within the gas tube or by means of surface ionization inwhich an ionizable gas impinges upon a hot cathode of a material whose work function is higher than that of the gas. Further, the plas: ma temperature may be established and maintained by additional means, if necessary, such as heating with an 7 electric field at the cyclotron frequency, or by means of thereby causing them to spiral about the center axis of the tube to establish the hollow electron beam. A hollow conproportioning the plasma electron temperature and electron density in accordance with the. above Equations 11 and- 12 so that the desired plasma waves will propagate with the desired phase velocity in the frequency range mw.k u where the negative energy beam wave also is present.

One of the advantageous features of achieving the ampassing a DC. current through some portion of the plasma. p I

An alternative embodiment of the invention is illustrated in FIG. 6 in which a hollow spiraling electron beam 40 is employed in place of the solid electron beam of the device illustrated in FIG. 5 The hollow spiraling beam is produced by means of an electron gun 41 which is comprised of a cylindrically shaped yoke member 43 which has an opening 44 at its left end, and a central rod 45 is centrally positioned within the opening 44 and joins the yoke member '43 at its opposite end. The yoke 43 and the center rod 45 are made of a magnetic material and a magnetizing coil 48 is wound about the center post 45 so as to establish a magnetic north pole at the right end of center post 45 and a south magnetic pole at the inner periphery of the open-end of yoke 43. In this manner radially-directed flux lines extend across the open end of the gun. An electron emissive cathode 50 is positioned within the yoke 43 and about the center post 45 so as to emit a tubular stream of electrons. When these electrons pass through an accelerating anode 51 and the radially-directed magnetic flux lines 'at the open end of the gun structure, a transversely directed force is exerted on the electrons ductive envelope 52 'is secured to yoke member 43 in a vacuum tight manner a similar manner to the beam collector electrode nib 55 is provided in conductive envelope 52 to permit the ionizable gas to be pumped into the device. The electromagnetic waves are coupled intothe beam-plasma interaction regions by means of a coaxial line coupler 56 which has a center probe 57 extending into the interior ,of the device. In a similar manner an output coaxial line coupler 58 having an inner probe 59 provides an output coupler for thedevice. An electromagnet! surrounds the conductive envelope 52 and establishes the longitudinal magnetic field B for confining the beam and the plasma. The operat-;

ing parameters for the beam and plasma are established in accordance with the above teachings. so as to achieve the desired interaction between a negative energybeam wave and is secured at its opposite end in and a positive energy plasma wave whereby the externally applied signals at a frequency near a multiple harmonic of the cyclotron frequency are coupled to a transverse electrostatic wave supported by the plasma, this Wave then being amplified by the transverse electrostatic negative energy beam Wave at the corresponding frequency.

FIG. 7 is another embodiment of the present invention, this device being illustrated as a Wave-wave type of amplifier. a solid beam of electrons is produced by the shielded electron gun 70 which may be the same type as described in connection with the device of FIG. 5. A permanent magnet 71 produces a magnetic field B that extends longitudinally in its central region and extends radially outward at its end regions. Upon entering the magnetic field B, the beam electrons are acted upon by a transversely directed force to cause them to assume a spiraling motion. The beam is collected at the right end of the tube by the collector electrode 72 after having passed through the plasma region 73.

Input waves at a frequency near a beam cyclotron harmonic frequency are coupled to a transverse electrostatic beam wave by means of the input coupler 75. Coupler 75 is comprised of two sets of three concentric cylinders which are fashioned from thin sheets of conductive material such as copper. The beam passes through the cylinders of each pair and has negligible intercept because of the thinness of the material from which the cylinders are made. The cylinders are spaced apart substantially an odd multiple of a half waveguide wavelength of the waveguide 84. Each set of cylinders of coupler 75 is excited in such a manner as to set up a transverse electric field of the waves to be amplified, and the two sets of cylinders are excited in phase opposition. That is, the signal to be amplified is split in phase by apparatus such as a T-junction, not illustrated, and the phase component is coupled by means of a coaxial line coupler 77 to the outermost and innermost cylinders of the first set of cylinders, and by means of coaxial line coupler 78 to the center cylinder of the second set. The phase component of the signal to be amplified is coupled by means of coaxial line coupler 79 to the center cylinder of the first set, and via coupler 89 to the outermost and innermost cylinders of the second set.

As discussed previously, the parameters of the beam and the magnetic focusing field B are proportioned so that a transverse electrostatic wave propagates on the beam at a frequency near a harmonic of the beam cyclotron frequency, this frequency being substantially equal to the frequency of the input waves to be amplified. With this condition prevailing, the beam passes through the transverse electric fields of input coupler 75 and the waves to be amplified are coupled to the beam. An ionizable medium such as cesium gas, as an example, is contained within a low loss dielectric tube 82, and the plasma temperature and electron density are proportioned as described above so that the plasma supports the type of waves'illustrated in FIG. 4, one of these waves falling within the range of the frequency of the waves to be amplified. Beam waves and plasma waves then couple together to give rise to amplification within the plasma region 73.

In this embodiment of the invention, the dielectric tube 82 is surrounded by a waveguiding structure such as the circular waveguide 84. The amplified waves propagating through the plasma region 73 of the tube will radiate outwardly from the plasma region, as depicted by the inclirred arrows, will couple into circular waveguide 84, and may propagate to a utilization device such as an antenna, for example. This demonstrates one of the advantages derived from the utilization of the transverse electrostatic waves near the multiple harmonics of the cyclotron frequency. That is, these waves have very high axial phase velocities and may directly couple into conventional transmission lines, thereby obviating the need for slow wave propagating and coupling circuits. Furthermore, because no special output coupling apparatus is needed,

the device of FIG. 7 may amplify to very high power levels without fear of power breakdown which is a common limitation in tubes that must employ special apparatus and circuits for coupling the amplified waves from the amplifier.

The above discussion has dealt with amplification that resulted from wave-wave interactions between selected beam and plasma transverse electrostatic waves having similar phase velocities. In accordance with the present invention, amplification of waves in the region of multiple harmonics of the cyclotron frequency also may be achieved by other phenomena which can be caused to occur within the beam-plasma system. A second type of amplification arises due to reactive instabilities that set-in in the beam-plasma system when the longitudinal dielectric constant of the plasma is less than zero (K O), in which case the plasma contributes inductive currents to the system and causes growth of the negative energy Waves of the beam. Suitable output wave coupling means then is provided for coupling to the amplified negative energy beam waves to launch amplified electromagnetic waves in an external device or transmission line. The value of electron density of the warm plasma that will make K O may be obtained by writing Equation 11 for the frequency an approximately equal to in which all terms refer to the warm plasma, and solve for the minimum value of w which causes the longitudinal dielectric constant to be less than zero. After taking into account the relative relationships between the plasmas parameters, the solution yields the following relationship for the plasma frequency u from which th plasma electron density may be derived,

The value of the square root term may be quite small in practice so that in this expression there is substantially no restriction on the magnitude of k This indicates that what is desired in order to have a reactive instability far above the cyclotron frequency with a weak plasma is a very long axial wavelength, A where A is related to k by the expression The value of plasma electron density required by Equation 13 is considerably smaller than would be required if the beam wave involved were a space charge Wave as employed in the prior art that is exemplified by the device described in US. Patent 2,806,974, for example.

The parameters of the beam of this device will be proportioned as indicated previously for the condition of stable negative energy transverse electrostatic Waves at multiples of the cyclotron frequency.

Any of the previously described devices of FIGS. 5, 6 and 7 may be employed to achieve amplification by means of the reactive instability phenomenon just described so long as the conditions of Equation 13 are satisfied for the plasma.

It also will be appreciated that amplification may be achieved as a result of resistive instabilities which arise when the longitudinal dielectric constant of the Warm plasma has a large imaginary value, that is, when the relationship a7mw is approximately equal to k u With these conditions existing the negative energy transverse electrostatic beam waves at multiple cyclotron harmonic frequencies will be amplified, this being somewhat analogous to the resistive wall amplifier, but operable at higher frequencies than the prior art resistive Wall amphfier whose operation is dependent upon amplification of short wavelength space charge waves as opposed to the long axial wavelength transverse electrostatic waves employed in the devices of this invention.

It should be understood that the above examples of the physical structures that may be employed in carrying out the present invention are merely representative of several ways of forming the required type of electron beam and for coupling to and from the transverse electrostatic Waves in the beam-plasma system. Other arrangements and combinations of electron gun structures also may be employed and will function in accordance with the above teachings so long as the indicated requirements of both the beam and plasma parameters are satisfied.

In the above discussion certain critical relationships were set forth in order to assure that the transverse electrostatic waves will stably propagate on the beam and plasma, thus assuring reliable amplifier operation. It should also be understood that if it is desired to provide a signal'source at the higher harmonics of the cyclotron frequency, the above development also will be instructed for this type of operation. As pointed out in connection with Equations 9 and 10, the electron density of the beam may exceed the relationships given in those equations so as to permit instabilities to arise on the beam, whereby the device then may function as a self-excited oscillatory source. Similarly, instabilities arising from the reactive and resistive nature of the plasma may be relied upon the device.

Although the above explanation of the interaction phenomena and the devices that have been described have dealt with electron beams in gas plasmas, the principles are applicable to other environments as well. That is, the fundamental requirement is that there be two bodies, or ensembles, of electrons. Therefore, the principles of this invention also may be applied to a double electron beam device, and to a photoconductive or doped semiconductor device through which an electron stream is passed.

While the invention has been described in its preferred embodiments, it is to be understood that the words which have been used are words of description rather than limitation and that changes within the purview of the appendedclaims may be made without departing from the true scope and spirit of the invention in its broader aspects.

What is claimed is:

1. Electron beam apparatus for providing output waves at a radian frequency w comprising,

input means to couple a signal to be amplified into said apparatus, means for producing a magnetic field fi directed along an axis,

means for producing a first ensemble of electrons having an axial drift velocity u and immersed in said magnetic field in a manner to cause the electrons of the ensemble to execute spiraling motions about axially directed flux lines of said magnetic field,

the parameters of said beam and magnetic field p being proportioned to produce a transverse component of electron velocity which approximately satisfies the relationship u; is the root mean square thermal velocity of the asecond ensemble of electrons disposed in energy couin said first ensemble of electrons, and

means for extracting wave energy fromtransverse electrostatic waves supported by at least one of said ensembles.

2. The combination claimed in claim 1 wherein said second ensemble of electrons has an axial drift velocity u and its parameters are proportioned with respect to said magnetic field B so that the following relationships are approximately satisfied and w 8w where m is the radian plasma frequency of the second ensemble and wherein the other quantities of 'said expression are as defined in claim 1 but relate to said second ensemble. 7

3. The combination claimed in claim 1 wherein the parameters of said second ensemble are proportioned to approximately satisfy the following relationship,

where u and w are, respectively the radian plasma and cyclotron frequencies of the second ensemble, k is the parallel Wave member of transverse electrostatic waves in said second ensemble, and a is the root mean square thermal velocity of second ensemble electrons in a direction parallel to said magnetic field, whereby said second en semble presents an inductive reactance to said first en semble.

4. An electron beam-gas plasma wave amplifying de passes means for producing a magnetic focusing field directly along an axis through said medium for immersing said beam and medium therein,

said beam being comprised of electrons that have a component of their velocity in a direction transverse to saidjaxis large enough to approximately satisfy the relationship where v, is the root mean square velocity of the beam electrons in the direction transverse to said axis, u is the root mean square thermal velocity of the beam electrons in a direction parallel to the axis, in is an integer, to is the radian frequency of Waves to be amplified, and tu is the radian plasma frequency of the beam, 7

whereby said beam will propagate transverse electrostatic waves at a frequency near a harmonic frequency' of the beam radiancyclotron frequency mg, said beam further being characterized by approximately satisfying the relationship w 8tu thereby to assure stable propagation of said transverse electrostatic beam waves,

means disposed adjacent said beam for supporting waves. with transversely directed electric fields in wave coupling relationship with transverse electrostatic waves on said beam, and

output coupling means for coupling to transverse electric field waves in said device. 1

5. An electron beam-gas plasma devicefor providing output Waves at a radian frequency w comprising,

signal to be amplified into said input means to couple a apparatus,

an ionizable gas medium contained within an enclo sure,

means for producing an electron beam that passes through said medium,

means for producing a magnetic focusing field directed along an axis through said medium for immersing said beam and medium therein,

said beam being comprised of electrons that have a component of their velocity in a direction transverse to said axis large enough to approximately satisfy the relationship where v is the root mean square velocity of the beam electrons in the direction transverse to said axis, a is the root mean square thermal velocity of the beam electrons in a direction parallel to the axis, In is an integer, w is the radian frequency of output waves from said devices, and tu is the radian plasma frequency of the beam, whereby said beam will propagate transverse electrostatic waves at a frequency near a harmonic frequency of the beam radian cyclotron frequency w means for ionizing said gas medium, and output coupling means adapted to couple to Waves having transverse electrical field components for coupling waves from said device to external utilization means. 6. The combination claimed in claim 5 wherein the parameters of said gas medium when ionized are proportioned to approximately satisfy the relationship where k is the axial wave number of electrostatic waves at the frequency w.

7. An electron beam-gas plasma wave amplifying device comprising,

an ionizable gas medium contained within an enclosure, means for producing an electron beam that passes through said medium, means for producing a magnetic focusing field directly along an axis through said medium for immersing said beam and medium therein, said beam being comprised of electrons that have a component of their velocity in a direction transverse to said axis large enough to approximately satisfy the relationship I)? m 1? b where v, is the root mean square velocity of the beam electrons in the direction transverse to said axis, a is the root mean square thermal velocity of the beam electrons in a direction parallel to the axis, m is an integer, in is the radian frequency of waves t be amplified, and w is the radian plasma frequency of the beam, whereby said beam will propagate transverse electrostatic Waves at a frequency near a harmonic frequency of the beam radian cyclotron frequency w said beam further being characterized by approximately satisfying the relationship w 8w thereby to assure stable propagation of said transverse electrostatic beam waves, means for ionizing said gas medium contained within said enclosure, means for coupling input waves at a radian frequency on near a frequency mw into said device in a region proximate said beam and plasma, said coupling means providing in said region transversely-directed components of the electric field of said input waves. 8. The combination claimed inclaim 7 wherein the parameters of said gas medium when ionized by approximately satisfying the relationship w 2w e where u and w are, respectively, the plasma and cyclotron frequencies of electrons of the ionized medium, k is the parallel wave member of transverse electrost-at waves in the medium, and a is the root mean square thermal velocity of the electrons of the ionized media, whereby said ionized gas medium presents an inductive reactance to said electron beam.

9. An electron beam-gas plasma wave amplifying device comprising,

an ionizable gas medium contained Within an enclosure, means for producing an electron beam that passes through said medium, means for producing a magnetic focusing field directed along an axis through said medium for immersing said beam and medium therein, said beam being comprised of electrons that have a component of their velocity in a direction transverse to said axis large enough to approximately satisfy the relationship where v, is the root means square velocity of the beam electrons in the direction transverse to said axis, u, is the root mean square thermal velocity of the beam electrons in a direction parallel to the axis, m is an integer, to is the radian frequency of waves to be amplifier, and ca is the radian plasma frequency of the beam,

whereby said beam will propagate transverse electrostatic waves at a frequency near a harmonic frequency of the beam radian cyclotron frequency w said beam further being characterized by approximately satisfying the relationship w 8w thereby to assure stable propagation of said transverse electrostatic beam waves,

means for ionizing said gas medium and for establishing a plasma electron temperature that approximately satisfies the relationship where k H is the axial wave number of waves at the frequency w and k n and a now relate to plasma parameters,

means for coupling input Waves at a radian frequency to near a frequency min into said device in a region proximate said beam and plasma,

said coupling means providing in said region transversely directed components of the electric field of said input waves.

References Cited UNITED STATES PATENTS HERMAN KARL SAALBACH, Primary Examiner. SAXFIEDD CHATMON, JR., Assistant Examiner.

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