|Publication number||US3719893 A|
|Publication date||Mar 6, 1973|
|Filing date||Dec 23, 1971|
|Priority date||Dec 23, 1971|
|Publication number||US 3719893 A, US 3719893A, US-A-3719893, US3719893 A, US3719893A|
|Original Assignee||Us Navy|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (2), Referenced by (10), Classifications (9)|
|External Links: USPTO, USPTO Assignment, Espacenet|
United States Patent [191 dePackh [451 March 6, 1973  SYSTEM AND METHOD FOR 3,626,305 12/1971 Furth et a1 ..328/233 ACCELERATING CHARGED PARTICLES UTILIZING PULSED Primary Examiner-Palmer C. Demeo HOLLOW BEAM ELECTRONS Attorney-R. S. Sciascia et a1.  Inventor: Davld C. dePackh, Oxon Hill, Md. T A  Assignee: The United States of Amerlca as represented by the Secretary of the Navy Filed: Dec. 23, 1971 Appl. N0.: 211,402
US. Cl. ..328/233, 313/63, 313/161,
315/111 Int. Cl ..H0lj 1/50, 1-105h 1/00 Field of Search..313/63, 161; 328/233; 315/111 References Cited UNITED STATES PATENTS 12/1969 Bodner ..3I3/16l X This disclosure is directed to a system for accelerating protons or other positive ions along with acceleration of a hollow beam electron ring. Hollow beam electrons normally have a high tendency to fly apart due to their own space charge; however, the positive charge ions accelerated therewith coupled with organized angular momentum prevents blow-up of the electron rings during acceleration. The magnetic field used for acceleration is particularly shaped so that the ions are not lost and the positive charge ions are accelerated with the electrons.
4 Claims, 10 Drawing Figures FIELD-REVERSAL PLANE HOLLOWBE AM ELECTRON \GENERATOR 23 H I If (I I? II n n 0 Hill I7 I fill II n i DIRECTION OF CURRENT IN WINDINGS FIELD COIL WINDINGS min I n n an r 7 ION- LOADED RING BEAM ADIABATIC DECOMPRESSION REG ION IIIIIIIIIIIIIIII RING AT MAXIMUM COMPRESSION BEAM WITH ANGULAR MOMENTUM AFTER FIELD REVERSAL SLEEVE BEAM WITHOUT ANGULAR MOMENTUM PATENTEDHAR 6l973 ,719, 93
ShEEI 10F 4 ASYMPTOTIC ORBIT FIG. la.
AXIAL MAGNETIC FIELD N WALL RESISTIVITY FORWARD VELOCITY Z ION COLLECTION REGION FIG.
PATENTEUHAR aim I 3,719,893
SHEET 20F 4 ZERO- ISOCLINE FIG. 4. FIG. 3.
SYSTEM AND METHOD FOR ACCELERATING CHARGED PARTICLES UTILIZING PULSED HOLLOW BEAM ELECTRONS BACKGROUND OF THE INVENTION This invention relates to particle accelerators and more particularly to the acceleration of positive protons or positive ions along with electrons.
Heretofore, various persons have conducted research on and proposed different systems for acceleration of positive charged ions with electron rings. Two such articles are Static-Field acceleration of Electron Rings by H. P. Furth and MN. Rosenbluth; Symposium on Electron Ring Accelerators, UCRL Report 18103, pp 210-218; and Some Prelimenary Thoughts on Ion Drag Accelerators, by W. Bennett Lewis, same Report 18103, pp 6-10. A system described in U.S. Pat. No. 3,506,866 sets forth a hollow beam electron ring generator.
SUMMARY OF THE INVENTION This invention is directed to an accelerator in which high current beams in the form of an electron ring in a vacuum environment with a strong focusing solenoid guide field accelerates protons or other positive ions. A high current electron ring accelerator generates pulses of electron rings which are accelerated into a vacuum environment having an axially aligned magnetic field. The electron ring pulses are accelerated into a field reversal region in which the electron beam is given angular momentum, compressed, and then into a compression region, where the beam is retarded. In this region the protons or positive ions are captured by the electron ring and accelerated along with the electron ring. Subsequent to the compression region, the combined electron ring and ions are accelerated into an adiabatic decompression region within which the ion loaded ring beam expands into a larger ring and is accelerated by a magnetic field gradient or by electron energy increase. Any well known electron and ion separators may be used to separate the ions from the electrons subsequent to acceleration.
STATEMENT OF THE OBJECTS It is an object of the present invention to accelerate a ring of electrons in such a manner that positive protons or ions are accelerated with the electron ring.
Another object is to provide an accelerator which has proper control fields for binding ions to an electron ring for subsequent acceleration therewith.
Still another object is to impart angular momentum to a ring beam of electrons to pickup and accelerate protons or positive ions.
Yet another object is to provide a linear accelerator which accelerates electron rings without blow-up of the electrons and without ions loose from the electron rings.
Still another object is to provide an accelerator which will acquire and accelerate a beam in a static magnetic-field.
While still another object is to provide an accelerator in which retardation of the beam is accomplished in a controlled manner by use of resistive walls.
BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic drawing of the resistive-wall ring retardation system.
FIG. la represents phase focusing due to the resistive wall for Z o.
FIG. 2 illustrates orbit collapse due to drag proportional to 1/V FIG. 3 represents ring current, I, as a function of the ratio of the ring radius, b, to the wall radius, a.
FIG. 4 represents a constant C as a function of the ratio of ring radius, b, to wall radius, a.
FIG. 5 represents wall current 1 as a function of the ratio of ring radius, b, to wall radius, a.
FIG. 6 represents angular momentum, 1,, as a function of the ratio of ring radius, b, to wall radius, a.
FIG. 7 represents a constant, C, as a function of the ratio of ring radius, b, to wall radius, a.
FIG. 8 represents angular momentum, J as a function of the ratio of ring radius, b, to wall radius, a, and
FIG. 9 illustrates a schematic diagram of the accelerator.
Now referring to the drawings there is illustrated a linear accelerator section for carrying out the invention. As shown, the system includes a cylindrical housing made of pyrex or any other suitable material which is provided with a means not shown for evacuation of the housing. The inlet end 11 of the housing is larger in diameter than the outlet end 12 and includes a central section of much less diameter joined to the end sections by conical sections 9 and 10 to form a constriction section or mirror region 13 from which the electron rings and ions are accelerated. The constrictive section 13 is coated on the inner surface with a resistive coating 14 the purpose of which will be explained later. An elec' tron ring or electron sleeve beam generator-accelerator 15 is secured to the inlet end for injecting pulses of electron sleeve beam 16 without angular momentum into a static magnetic field. The static magnetic field is produced by coil windings 17 to which a direct current denoted by arrow 18 is applied for providing an axial magnetic field 19 in the direction of the electron direction 20 as shown by the arrows.
Adjacent the coil windings 17 there are coil windings 22 which surround the end of housing section 1]. Along the conical sections 9 and 10, the central constricturesection 13 and the adjacent end 12 of the out let section D.C. current denoted by arrow 23 is passed through coil 22 in the reverse direction from that of coil 17 produce an axial static magnetic field 24 in the opposite direction and equal magnitude. The magnetic field-reversal plane is indicated by the dotted line 25. The magnetic field strength aiong the central housing section denoted by arrow 26 is much stronger than that of the field at arrow 24 in order to form a compression region. The magnetic field toward the outlet end is decreased from that of the central region and is shown by arrow 27. The length of the arrows denoting the direction of the magnetic fields represent the comparative field strengths. The arrows indicated by a V indicate the electron direction, and H, the magnetic field direction. Lengths of H-arrows indicate relative mag netic field strengths.
In operation, the system is evacuated, the magnetic fields are developed and the electron sleeve beam generator-accelerator is made operational to produce electron sleeve beam pulses of typically Mev that are injected into the field reversal section of the system as rapidly as possible. The sleeve beams are coaxially aligned within the housing without an angular momentum as they are accelerated through magnetic field 19. This requires that the cathode of the electron source be within the magnetic field. The sleeve beams are accelerated through the first magnetic field area into the second magnetic field which is in reverse direction to the first magnetic field. As the sleeve beams are accelerated into the area of the reversed magnetic field, the sleeve beams are slowed down, contracted into shorter-length cylinders and an angular momentum is imparted to the electron sleeve after field reversal. The electron sleeve beams are further contracted and compressed into a smaller-diameter shorter cylindrical shape as the beams enter into the central section 13 which has a much greater magnetic field. The walls along this section are resistive to provide controlled beam retardation. Since the magnetic field strength along section 13 is much greater and angular momenturn is imparted to the electron beams, the forward velocity of the electron beams in this section will be very low. Therefore, the beams will spend a long time in this section. It is in this section that the ions in the residual gas are captured by the electron beams and subsequently accelerated with the beams. The electron ring is prevented from flying apart by the ions to be accelerated and by the angular momentum of the electron rings. The angular momentum permits the number of positive charges to be materially less than the number of electrons.
From the compressed area, acceleration of the electron ring and the captured ions must be done carefully to avoid shaking the ions loose from the electron rings. Therefore, final acceleration may take place by simple adiabatic decompression. Additional acceleration may be provided by means of an accelerator following the adiabatic decompression region. In moving from the compressed central area where there is a strong magnetic field the electron ring-ions will move into a magnetic field of less intensity as the particles move from the compressed area. The electron ring will expand in diameter and the combined particles will be accelerated to a desired velocity and separated by electron and ion collectors which are well known in the art.
The successful operation of this system as an electron ring-ion accelerator depends on the control of the electron sleeve beam in the field reversal region. Therefore, the magnetic field must be carefully shaped, controlled and applied in order to prevent the electron ring and ions from being forced back toward the electron accelerator.
The system has been shown with resistive walls 14 along the constrictive section 13. These resistive walls provide a means of controlling the ring motion in this region. For a correct choice of the different parameters, resistive drag is proportional to ring velocity. The effect of such a velocity dependence is to render the minimum velocity, where ion trapping occurs, less sensitive to residual errors in electron energy, magnetic field, and other parameters than would otherwise be the case. if, for example, the ring is handled altogether conservatively and adiabatically from the field reversal region onward, one has where R H is an adiabatic invariant. Thus at minimum (subscript 0) one has where H, is H just beyond reversal and H is the field at the mirror. Ions are subject to an accelerating field of the order of 0.6 Mv/cm for nominal ring parameters (minor radius 1 mm, i 1000 amp), which corresponds to an energy of 0.06 Mev B= 0.01 for protons and correspondingly lower for heavier ions at the ring boundary. Thus B0 10"; if-y R, H H are supposed independent, the same order of accuracy is required of all these quantities. This, of course, is a statement of the fact that the mirror point is unstable.
in considering the motion of such an elementary charge ring one can imagine the force to be made up of a number of components; thus one can write.
where the accent means a partial z-derivative and A, B, C are constants. This equation represents the most important external forces acting on the ring. The first term is the dipole force due to the external field gradient, the second proceeds from electric or magnetic images in partially conducting walls; the third may have a similar origin, and it also includes any space-charge drag forces produced by positive ions which are left behind. The detailed character of these forces will be taken up later. Here we consider the general effect of each term.
With respect to the first term one sees that the axial field acts like a potential. If B C 0, the equation integrates once to give v, :(vf 21111,
If v is the final velocity, at the peak field, then A real beam with a spread in both 2 and [3, goes through a minimum extension in z before reaching the mirror. One expects the velocity spread to be gradually translated into a spread in position A z roughly according to the approximate relation where ?is the mean time for the ring to pass into the mirror, i is the average velocity in this region, and z. is an effective length of the order of the mirror thickness. As the axial spread due to initialAv grows with the approach to the mirror, the spread due to the original axial extension diminishes. From this cause The minimum extension should occur where these twoAzs are equal, thus where One can roughly take v r, since the ring spends most of its time near the region of least velocity. This gives All these results suggest that ifAv,,/v is kept to the order of IO, the resulting ring has a satisfactory behavior at a final velocity of order 0.0lc, but if the final velocity in the conservative region could be increased to 0.20, the tolerance could be increased to -4 percent.
If the term Bv is included in the equation of motion, the system is of course no longer conservative. One notes first that if the rate of slowing down of the ring is small, the velocity is asymptotic to the value Since A, B, and v, are all positive, one requires H, 0. Thus if the drag force corresponding to the term --Bv is to be used to control the velocity, the principal retardation by this effect occurs on the far side of the mirror.
On emergence from the cusp, B is still rather near 1. This follows from the fact that if large orbit perturbations due to transmission through the cusp are to be avoided, 13 after transmission should not exceed about 0.5. On the other hand, if rather large energy losses are not to take place, B on entry into the resistive drag region should not exceed about 0.5. Thus for z 0, say, B (perfectly conducting walls). One then matches the wall resistance and field gradient to the condition (forfi, 0.5 going into the drag region) so that conservation of forward momentum requires that after ion collection v,
If it is desirable to offset this effect, the axial field can be reduced in the collection region, though there is no obvious reason for doing so.
The nature of the phase focusing provided by the resistive drag can be understood by consideration of the asymptotic orbit for the equation dv ldt --AH Bv which approaches zero velocity as A 0. In first approximation this is just In the next approximation one can substitute this value of v,.on the lbs of the differential equation to get a second approximation The particular orbit which is approached by this successive approximation procedure is asymptotically approached by other orbits in its neighborhood (FIG. 10). Thus, phase space injected near this orbit becomes concentrated on it, as the figure schematically shows. Since there is then ideally negligible phase space at right angles to this curve, one then expects the approximately 50-fold shortening in the z-direction predicted by simple theory in going from B, 0.5 to ,6, 0.01 for the example chosen.
Resistive drag produces a reduction of the compression achievable in a system without it. The compression ahead of the mirror (conservative) is where [3 is B, at the entrance to the resistive region (peak H and B is [3 at the emergence from the cusp. This is a rather small reduction with respect to the H3, which would result from slowing the ring down conservatively to a very small forward velocity for any reasonable value of B Because the velocity is given approximately by (A/B)H,', the principal slowing being caused by a graded increase of B, there is a definite drop in the field produced by nonvanishing H The time required to approach the asymptotic orbit is, however, independent of H being given approximately by 1/B; thus, the characteristic distance for approach to the orbit is v lB. On the other hand the system length L is of the order AAH,/B,, as follows from the first approximation to the asymptotic velocity. It is required that L should be much greater than the characteristic distance for approach to the asymptotic orbit; thus This relation indicates that the field drops in the drag region by twice the amount by which it would increase if the slowdown were carried out conservatively (since conservatively Now it will be shown that the energy loss in stopping the ring is given approximately by also A b i /N 'ym, where b is the ring major radius and i, is the current. One has Ab/b =A-y/'y- AH IH ;/3,}+v, /AH /&B, k5, =0 if one takes B= l and uses the limiting value of AAH, given by v}. In practice -AAH must be several times larger than this so that Ab/b should be several times 3,. If B, is as much as 0.5 this could result in an appreciable increase in radius.
The third term in the force equation -C/v, represents an unstable drag force since it increases without bound as the velocity diminishes. It is therefore important to know how large C can be before this force seriously affects the motion. Orbits which collapse toward zero velocity exist outside the zero-isocline given by -AH,' Bv C/v,
(See FIG. 2). The minimum value of-AH, is
i.e., if -AH falls below the value, velocity collapse is to be expected. If the C-term is small except in this neighborhood, one has -AH '-Bv so that approximately one must satisfy v, 2(C/B) MAGNETIC DRAG In considering magnetic drag one supposes a filamentory current ring of radius b in a tl be oirgiius a. The ring moves along the z-axis with a velocity v,, c and is centered in the tube. The components of magnetic field and flux are numbered 1 or 2 according as they result from ring or wall current. The primary flux produced by the ring at z,(t) and linked by an elementary ring of the wall at z is 1 1 i,,M(b,a,z,z,) E i,,(ab)" m(b/a,(z-z,)/a) E i,,(ab) m(b/a,), where i, is the ring current. M is the mutual inductance, and m is the normalized mutual inductance. Tables of m in terms of elliptic integrals may be found in inductance calculations by F. W. Glover, Dover, New York 1962, p. 77.
The secondary flux produced by all wall rings and linked by a ring of radius r at axial position z is where u i (zz,)/a and at the wall.
Combining Ohms law and the gives j is the surface current density continuity equation yd l )l-yaz, (21ra/-yv )j= 'yq /'yz,. The longitudinal force on the ring is where m means 'ym/yf. One can of course also calculate the Force on an isolated subring z,) if one wants to consider the focal properties of the system, it is sufficient at this point to note that the force is greatest at the ring position so that the focal equilibrium is neutral as far as the drag forces are concerned. It will appear below that, although the drag forces (resulting from nonvanishing wall resistivity) have a neutral equilibrium, the image contribution from the perfectly conducting wall terms does have focal properties. Case a: is small.
I, is shown in FIG. 3. Case b. :0 is large.
The current densityj and the secondary flux are divided into zeroth and first order components; the zeroth order part is the contribution associated with a perfectly conducting wall. Then 'Y 21( )/'Y r 'Y 21 )172 z)jo- I One needs the solution of the Integral equation where C(b/a) is shown in FIG. 4. The perturbation requires a solution forj,. One has This has the same form as the tion; therefor preceding integral equa- (was),
f..= w ver/ v.) (war f; M w/a. m:
Using this value, one finds an upper bound to the force to be As a typical value one might take b/a makes the upper limit 0.8, which for the current in emu; the corresponding value of v is about 0.2. Thus, if v, 0.050, the surface conductivity at the transition is 1.3Xl0- emu 0.13 mho. To insure a drag force proportional to velocity the conductivity should be substantially below this value. The distance required to stop the ring, using the upper bound on the drag and a current of 1000 amp emu and an initial velocity of 0.050, with 10 electrons in the ring and y=20, is
Thus, the magnetic drag is entirely adequate to slow the ring in a reasonable distance by a suitable choice of resistivity.
' ELECTRIC DRAG The axial electric field produced by the ring charge Q at at the wall point (z,a) is where The axial field produced by the whole wall charge at the point (r,z) is where S is the wall charge per unit axial length. If the surface resistivity is p, Ohms law and continuity give 'YE2( lvz l w/ 1 /72 W I/12 where dz,/v, has been written for dt. With the quasistatic approximation 'y/yz-'y/'yz, this equation immediately integrates to give The longitudinal force on the ring is f., Qu Case a: p is large.
Case b: p is small.
E 1 E (zero order) E (l)= (pv /Z'n'a) S (first order);
S solves the integral equation (The surface charge in zero order could of course also be found by setting it equal to V411 times the primary radial field at the wall, thereby avoiding the integral equation. With the approximations used here there is no gain in introducing the radial field.) The perturbation requires a solution for S One has This has the same form as the preceding integral equation; after appropriate integrations,
The force is (after integrating by parts) The quantities J,, c, and J are shown in FIGS. 6, 7, and 8.
The transition between high and low resistivity is at and the upper bound on the force is given by If one again uses b/a 0.8 as an example, setting Q, 21ri,,b, one finds for the upper bound The magnitude of this force is therefore the same as the magnetic force. The resistivity at transition for v 0.05c is about 5 X10 esu or about 4,500 ohms/square. To insure an electric drag force proportional to the velocity the resistivity should be materially below this value. It was shown that the same velocity dependence could be achieved by means of magnetic drag (for the same velocity) if the resistivity exceeded about 7 ohms/square; there is therefore a range of resistivities in which both forces have the correct behavior. One also notes, however, that if the resistivity is set at the geometric mean of values, or about 200 ohms/square, the stopping distance is only about k X (4500/200) X 0.012 -0.l cm,
which is obviously prohibitively short. It therefore appears to be desirable to use one of the two mechanisms while suppressing the other by means of slots in the coating.
ENERGY LOSS The loss of energy is easily calculated by means of energy and momentum balance. Thus we have whence after an integration The electron energy loss is therefore small as long as B 3. Even for B, 0.5 the loss is only 13 percent, and it drops with the square of the velocity. Drag Due to Abandoned Ions The number of ions formed per cm of electron track is Nno', where n is the neutral density and o' is the ionization cross section. There, the number per axial cm is Nno'lfiz. To simplify matters one assumes that M= LNn /2 11b 5,.
The total drag force is therefore if in order of magnitude we take z L, the drag force then becomes ZN e no'lrrbfi The ion drag coefficient C is then given by If one supposes that electric drag is the chosen mechanism, one has for the coefficient B so that the condition for freedom from abandoned-ion effects becomes If one takes o= l0' cm o'= (l/9) 2 ohms/square, Z l, and a pressure of mm, one finds for this requirement v, 3 X l0 cm/sec.
Accordingly lf one is to reduce the ring velocity to about this value, it is desirable to have a pressure of an order or so lower, i.e., about 10 mm. This calculation should be done with greater accuracy if exact pressure limits are to be established. Focal Effects in the Resistive Region For an unnuetralized ring beam close to the wall one can estimate the zeroorder (perfect-conductor) force on a sub-ring using simple image considerations. If the center of gravity of the ring section at (r,0) is at a distance s from the wall and one considers the z-col'nponent of force on a filamentary sub-ring at (r,e) with charge density )te per unit length, and if in addition one supposes the wall to be longitudinally slotted so that there is no magnetic image, then the axial force per unit azimuthal beam length is Thus, electrostatic defocusing dominates at distance there is a short-range axial defocusing followed by axial focusing at greater distances. The whole ring would of course be radially unstable because of the attractive force of the image except for the external magnetic field. On comparing the radial force on a sub-ring (charge linear density A, position (r e, 0)) due to the combined effects of the image and the main ring (it, (r,0)) on the one hand with that produced by the'external magnetic field on the other, one has for the first force per unit azimuthal length a quantity of order.
)Jflelx for c of the order of s (short-range defocusing of course always exists); for the second force one has A'eH The first can thus be neglected if on using the relations 'y=)te /mc H b 'ymc le. This requirement should be rather easily satisfied.
The effect of short-range defocusing in both axial and radial directions is to give the ring a nonvanishing cross section. The radial part is included in a more general radial smearing-out which takes in the acceptance phase space, the sc alloping due to the cusp, and the like. The axial part is included in the axial extension due principally to energy spread. If the above numbers are accepted as order-of-magnitude estimates, then Both of these are well below what would be expected of the normal phase space spread.
The magnetic image is defocusing in the axial direction, and its use is therefore not indicated. The use of a longitudinally slotted wall, because of its suppression of azimuthal currents, should be of some effect in the suppression of azimuthal resistive-wall instability.
What is claimed and desired to be secured by Letters Patent of the United States is:
means relative to said conical sections, said smaller diameter section and said second section for producing second axially aligned magnetic field in a reverse direction from that in said first section,
said second magnetic field increasing in strength along the conical section on the inlet side of said smaller diameter while decreasing from said smaller diameter section toward the outlet end said second magnetic-field strength along said smaller diameter being of uniform strength and much greater than said first magnetic field, and
means for injecting pulses of hollow beam electrons into said inlet end, into said first magnetic field for acceleration by said first magnetic field into said second magnetic field.
2. An accelerator system as claimed in claim 1;
the inner wall surface of said smaller diameter section of said housing has a resistive coating thereon.
3. An accelerator system as claimed in claim 2;
said outlet section provides an adiabatic decompression region through which positive ions are accelerated along with hollow beam electrons.
4. A method of accelerating positive ions along with pulses of hollow beam electrons which comprises,
evacuating an accelerator housing,
injecting pulses of hollow beam electrons into first axially aligned magnetic field with the direction of the magnetic in the same direction as the direction of movement of said hollow beam electrons,
directing said hollow beam electrons into a second axially aligned magnetic field whose direction is reversed from said first magnetic field and opposite to the direction of travel of said electron beam whereby angular momentum is given said electron beam,
increasing the magnetic field strength toward a smaller housing section,
maintaining said magnetic field at said increased strength along said smaller housing section and adding ions to said electron beam confined by said magnetic field along the smaller housing section,
decreasing said second magnetic field in an axial direction from said smaller housing section to a larger outlet section which forms an adiabatic decompression regions,
maintaining said magnetic field steady along said outlet section and directing said combined ion-hollow beam electron pulses into said adiabatic decompression region from which the ions and electrons are accelerated.
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|U.S. Classification||315/500, 313/161, 376/127, 313/359.1, 376/129|
|International Classification||H05H1/54, H05H1/00|