Production of billion electron volt potential wells by cloud of electrons suspended in magnetic fiel

Janes, G. S.

Levy, R. H.

Petschek, H. E.

English

NASA Technical Reports Server

AMP 166 
THE PRODUCTION OF BEV POTENTIAL W E L L S  
G. S. Janes ,  R. H. Levy andH.  E. Petschek 
AV C 0 - EVER ET T R ESEARCH LAB ORA T ORY 
a division of 
AVCO CORPORATION 
Everett ,  Massachusetts 
June  1965 
supported jointly by 
HEADQUARTERS 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
OFFICE OF ADVANCED RESEARCH AND TECHNOLOGY 
Washington 25, D. C. 
under Contract No. NASw-1101 
AIR FORCE OFFICE OF SCIENTIFIC RESEARCH 
OFFICE O F  AEROSPACE RESEARCH 
UNITED STATES AIR FORCE 
Washington 25, D. C. 
under Contract No. A F  49(638)-1553 
https://ntrs.nasa.gov/search.jsp?R=19660007433 2020-03-16T23:06:53+00:00Z
It may be possible to produce large electrostatic potential wells 
by a method which avoids the usual breakdown limitations. 
be produced by a cloud of electrons suspended in  a magnetic field. 
mental  and theoretical  evidence bearing on the stability of such clouds a r e  
discussed by Janes.  
Bev range may be accessible with large equipment. 
the potentia1,well would be both accelerated and contained. 
of ions which can be contained in this way is  limited by the accumulation 
of positive space charge,  it would be possible to produce an  overall reaction 
16 rate  of the order  of 10 While the concept 
of achieving high energy nuclear reactions at such enormous ra tes  is  very 
appealing, it should be borne in mind that the entire concept is s t i l l  in  its 
The well would 
Experi-  
Estimates to be presented below suggest that the 
Ions introduced into 
If the number 
nuclear reactions pe r  second. 
infancy. Thus, although preliminary low voltage 
analyses a r e  very  promising, serious obstacles 
tions may yet be discovered. 
2 
experiments' and stability 
to achieving these condi- 
The overall  configuration i s  sketched in  Fig. 1. An electron cloud 
is  contained along the circular  axis of a torus  by a magnetic field paral le l  
to  this axis. This cloud produces a potential minimum along the circular  
axis and an  electr ic  field in the direction of the minor radius. Individual 
electrons rotate in the E x B direction around the circular  axis at the E/B 
velocity. 
jecting the electrons onto magnetic field lines a s  the magnetic field i s  built 
up. The magnetic field lines then c a r r y  the electrons into the system re -  
placing the belt in a Van de Graaff. 
The electron cloud can be introduced into such a system by in- 
1 
POSITIVELY CHL\RGED 
I 
I 
I 
I 
I 
Fig .  1 Illustration of the toroidal geometry discussed in the text. 
-2- 
The ordinary breakdown limitation of surface discharge i s  obviated 
since there  is no insulator separating two electrodes. Fur thermore ,  the 
limit assoc ated with field emission of electrons f rom the negative terminal  
is also eliminated. If the breakdown limit  i s  associated with ion extraction 
f r o m  the outer wall, e lectr ic  fields in  excess of 10 v/cm should be attain- 
able. 
8 
The equilibrium for containment of the electron cloud i s  obtained 
by balancing the electr ic  and magnetic s t r e s ses  on the individual electrons 
(E + v x B = 0). Coupled with Gauss 's  and Ampere 's  laws, this reduces to 
a balance of the sum of the magnetic and electrostatic s t r e s ses .  
e lectron densities, o r  more  precisely if  / W  (plasma frequency/cyclotron 
frequency) << 1,  inertial  s t r e s s e s  a r e  neglible. 
field i s  unaffected by introducing the electron cloud. 
the speed of light the magnetic field i s  decreased in the region of the elec- 
t ron  cloud. In order  to demonstrate quantitative relationships for this con- 
tainment, lines of constant magnetic field intensity, e lectr ic  field intensity, 
and electron density have been plotted in F ig .  2 on coordinates of E/B ve- 
locity (expressed in r e s t  energy t e rms)  and total depth of the potential well. 
The figure is drawn for a torus  of one meter  minor radius,  and a l l  quanti- 
t i es  a r e  measured  at  the outer edge of the plasma. 
would lead to la rger  voltages. 
Fo r  low 
P C  
If E/B << c ,  the magnetic 
As E/B approaches 
Larger  apparatus s izes  
Ions injected into the system wi l l  be accelerated to an energy equal 
to the depth of the potential well o r  to an energy corresponding to the E/B 
velocity, whichever is lower, as indicated by the dotted lines in  F i g .  2. 
The ion density which can be built up before the potential well i s  destroyed 
- 3- 
2 ‘/2 
DRIFT KINETIC ENERGY/m,C*, [ (I-%)- -I] 
I I I I I I I 
3 x IO-’ I d 2  3 x to-* lo-‘ .3 .6 .9 
v/ c 
F i g .  2 Map of 1 meter  electron plasma containment device. The shaded 
region is thought to  be accessible.  
-4- 
A3820  
. . 
by positive space charge, o r  before neutral  plasma forms of instability 
become important may be comparable to the initial electron density. 
Figure 2 has been terminated along a line (0 2/Oc2= 1) for which 
P 
the electron gyro radius based on the E/B velocity, r e ,  is equal to the 
minor radius,  a, since this is an absolute limit to containment of the elec- 
t rons  by the magnetic field. Low voltage experiments” suggest that there  
2 2  i 
may be an  instability i f  0 /wc becomes greater  than about 0.05. The 
lower boundary of the shaded region represents  a crude estimate of a 
limitation imposed by this instability. The upper boundary of the shaded 
region i s  determined by the upper s t r e s s  limit to the strength of magnetic 
5 field which can be achieved ( -  2 x 10 The shaded a r e a  then rep- 
, 
gauss). I 
resents  a n  estimate of the accessible region. 
The upper corner  of this region corresponds to ion densities in  
and ion energies comparable with 1 Bev where the 
16  
11 - 3  c m  excess  of 10 
total meson production rate  should exceed 10 
c r o s s  section of 10 - 2 5  c m  and a system volume 10 
per  second based on a 
2 8 3  c m  . Since the ions 
move in random directions, the center of mass  velocity may be small  and 
in  many of the above cases  can lead to available C.  M. energies in excess  I 
of the threshold for heavy anti-particle production. 
for  anti-particle production a r e  of order  10 c m  , one might expect a 
total  yield of anti-particles i n  the range of 10 
Since the c r o s s  sections 
- 2 %  2 I 
13 per  sec.  , 
Since anti-protons will primarily be created near the center where 
i 
E/B2 i s  small ,  there i s  some possibility of containing them in the magnetic 
field despite their negative charge. i 
- 5 -  
These considerations represent a considerable extrapolation f r o m  
understood regions. Prel iminary experiments’ have been ca r r i ed  out a t  
voltages l e s s  than 10 kV, with E/B velocities less  than one-hundredth the 
velocity of light, and with somewhat different geometries. Similarly, 
theoret ical  stability analyses 2 have been restr ic ted to neglecting the elec- 
t ron  mass ( W  /O << l ) ,  E/B <<c, and assuming no spread in  electron ve- 
P C  
locity at a point. 
tive charging principle and have demonstrated a stable range, no definitive 
statement can be made regarding extrapolation to the conditions discussed 
above. 
bility in  this ca se  than has  been found for neutral  plasmas.  
plasma is charged, disturbances in  the plasma make significant fields 
a t  the container walls. 
by adjusting the wall impedance can produce fields in the plasma which 
stabilize the disturbance. These image charges apparently stabilize in 
the region which has been studied. 
Thus, although the experiments have verified the induc- 
In very  gross  t e r m s  there i s  some reason to expect greater  sta- 
Since the 
Either the natural  image charges o r  fields obtained 
2 
We  may also note that an interesting facility can be obtained on a 
much smaller  scale and with less extrapolation f rom known conditions. 
The upper limit of voltages obtainable with a Van de Graa f f  - 10 Mev can 
be reached with a torus  of 10 cm minor radius,  a t  magnetic fields of 
5 x 10 
E/B i s  st i l l  smal l  compared to the speed of light (-lo-’) .  
‘/Wc2 < . 05. At this condition G a u s s  including the restriction W 4 
P 
-6- 
b 
1 .  
2. 
3 .  
REFERENCES 
Janes, G . S . ,  "Experiments on Magnetically Produced and Confined 
Electron Clouds, I' Avco-Everett Research Laboratory AMP 165, 
to be published in  Phys. Rev. Letters.  
Levy, R. H. , "The Diocotron Instability in a Cylindrical Geometry, 
to be published Phys.  of Fluids, Vol. 8,  No. 7 (July 1965). 
Knauer, W. and Stack, E. R. , "Alternative Ion Pump Configurations 
Derived f r o m  a More Thorough Understanding of the Penning Dis-  
Charge, " Transactions 10th National Vacuum Symposium held in  
Boston, October 1962. 
I 
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