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Proceedings of RuPAC XIX, Dubna 2004
NEW METHOD OF ELECTROSTATIC ACCELERATING AND STRONG
QUADRUPOLE FOCUSING OF CHARGED PARTICLES ON HIGH
VOLTAGE ACCELERATORS OF DIRECT ACTION AND ITS POSSIBLE
APPLICATIONS
N. I. Tarantin, JINR, Dubna, Russia
Abstract
The present report proposed a system of electrodes for
sign-alternating strong electrostatic quadrupole focusing
of intense beam of charged particles and their
simultaneously direct accelerating. This system is
defended of the patent [1].
INTRODUCTION
Modern charged-particle accelerators utilise some strong
focusing principles, which is achieved by using an
azimuthally variation of the magnetic field in the circular
accelerators, alternating of the sing of the magnetic field
gradient in the ring-racetrack accelerators and using a
high-frequency quadrupole accelerating electric field in
resonance linear accelerators. High-voltage chargedparticle electrostatic accelerators of direct action use socalled weak electrostatic focusing by a fringing electric
field.
This raises the question whether strong focusing by a
static electric field in the linear electrostatic accelerator of
direct action.
ANALYTICAL MODELLING OF AN
ELECTROSTATIC ACCELERATING AND
STRONG QUADRUPOLE FOCUSING
SYSTEM
and also Krylov-Bogoliubov’s asymptotic approach
method .
From equation (2), we have ∂Eϕ (r,ϕ,z)/ ∂ ϕ
=-∂[rEr(r,ϕ,z)]/∂r, on integrating of which we obtain
Eϕ(r,ϕ,z)= -2Grrϕ
(4)
Substituting result (4) into equation (3) we have
∂Er(r,ϕ,z)]/∂ϕ=∂[rEϕ(r,ϕ,z)/∂r, integrating of which we
obtain
Er(r,ϕ,z)=Grr[1-(2ϕ)2/2]
(5)
Using result (5) and equation (2) and again integrating we
obtain Eϕ(r,ϕ,z)= -Grr[2ϕ-(2ϕ)3 /3!].
In the end, continuing in such a manner and using series
for sin2ϕ and cos2ϕ we come to
Er(r,ϕ,z)=Grrcos2ϕ, Eϕ(r,ϕ, z) ==-Grr sin2ϕ,
Ez(r,ϕ,z)=Ez
(6)
Thus we have obtained electric field (6), that is either
linear focusing or defocusing of the charged particles by
the electrical gradient of Gr in the cross-sectional plane
and constant accelerating along the Z-axis by electric
field Ez.
Taking the integral at (6) we have the potential of
analytically constructed field
V(r,ϕ,z)=V(0,0,z0)-(z-z0)Ez-Grr2cos2ϕ/2
(7)
We consider the inverse problem solving for analytical
constructing of electrostatic systems with a given field
structure. This problem includes a three-dimensional
analytical expansion of the basic electrical field, for
example,
where V(0,0,z0)-field potential in initially point laying on
the Z-axis.
Electrical potential (7), as can be shown, is solution of
the Laplace’s equation.
From (7) it follows that internal profile of any monopotential electrode for this field must satisfy the following
equation
Er(r,0,z)=Gr r, Eϕ (r,0,z)=0, Ez(0, 0, z)= Ez (1)
re(ϕ,z)=±{2[V(0,0,z0)-Ve-(z-z0)Ez]/Grcos2ϕ}1/2
in cylindrical coordinate system. Field (1) accelerates
positively charged particles along Z- axis at Ez>0,
focusing (Gr <0) or defocusing (Gr >0) them relative to the
Z-axis in the plane ϕ=0.
For a three-dimensional analytical expansion, we use the
Maxwell’s first order differential equations solving which
is simpler than Laplace’s second order differential
equation solving:
where re(ϕ,z) is the radius-vector describing the internal
profile of the electrode, Ve is the electric electrode
potential.
A schematic picture of electrode cross sections can be
seen in Fig. 1 for two quasi-cylindrical electrodes 1 and 2
as the projection onto three planes: z=const, ϕ=0,z and
ϕ=π/2,z. It shows electrodes made from a metallic sheet.
Number 3 is electrode metallic keeper, amin and amax are
the minimal and maximal semy-apertures of the
electrodes.
divE=0
(2)
rotE=0
(3)
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Proceedings of RuPAC XIX, Dubna 2004
Energetic Application
Figure. 1: Quasi-cylindrical electrodes for the high
voltage accelerator of direct action that enable the
electrostatic accelerating and strong quadrupole focusing
of charged particles.
PARAMETERS OF QUASICYLINDRICAL QUADRUPOLE
ELECTRODES
For the given accelerating electric field Ez=20 kV/cm, the
gradient of radial components of focusing electric field
should be equal to Gr=±35 kV/cm2, which is about 10
times higher then the gradient of weak electrostatic
focusing. Let us choose 2amin=3.0 cm. Then the electrode
length can be l = 4.5 cm and maximal aperture of the
electrodes 2amax=5.4 cm. For these parameters, the of
maximal electric field on the internal surface of electrode
will be no more then maximal admissible field in a
vacuum, which is 100 kV/cm. For the given quadrupole
field with Gr=±35 kV/cm2, the potential of VF=39.8 kV
relatively to the potential of the Z0 -point is required for
the electrode for focusing positively-charged particles and
the potential VD=-129.8 kV for defocusing. The
difference in the potentials of the neighbouring electrodes
along the Z- axis is ∆V=2 VD for the FD gap and ∆V =2
VF for the DF gap.
It can also be used to create an efficient accumullatorcollider of accelerated deuterium and tritium ions for
neutron generation in vacuum collisions of two merging
beams for energy generation by means of sub-critical
nuclear reactor driven by an accelerator [2-6] and for the
transmutation of radioactive nuclei. The confinement,
accumulation and colliding of accelerated ions take place
in crossed magnetic field and electrostatic field of a
solenoid and a three dimensional octupole.
It is propose to use the phenomenal reaction D +T= 4He
+ n having a very large resonance cross section (5.0 b) at
a very low energy (63.0 keV in the centre-of-mass frame).
Head-on-tail collisions at equal orbital moments are
considered. In this case atomic ions of deuterium and
tritium need correspondingly 0.90 and 0.63 MeV of
energy. The physical cost of one neutron is 1.5 MeV,
which essential smaller than that for the known
electronuclear generation of neutrons by bombarding
heavy targets with energetic accelerated deuterons.
A high total electric current of the negative hydrogen
ions (~1A) can be produced by using 16 of special ion
source. . The acceleration of these ions to required
energies with high beams electric current can be carried
out by 16 small electrostatic accelerators of direct
operation. These currents can be accepted by ionic trap
with high acceptance created by the end fringing
magnetic field of the solenoid. Then it is follow stripping
of two ionic electrons inside the trap by an electron beam.
The high stability of ion beams in the crossed magnetic
and electric fields of the trap are is ensured by the
absence of so-called secular instability of rotating ions.
This low-energy electrostatic accumullator-collider of
accelerated deuterium and tritium ions allows creating a
continuos neutron flow of an intensity of ~1019 s-1 and can
be used as the driver of a subcritical nuclear fission
reactor operating on minor actinides with the coefficient
of fast neutron multiplication k=0.975 for production of
some GW of commercial electric power.
POSSIBLE APPLICATIONS OF THE
ELECTROSTATIC ACCELERATING AND
STRONG FOCUSING METHOD
Direct Application
Direct application of this method is using it for
transmission of intense charged particles beam in
electrostatic accelerating devices of direct action - in
accelerators for physical investigations and for practical
aims and also in ion implantators for technological
applications. For example, direct electrostatic accelerator
for obtaining intensive proton beam (~100 mA) of energy
~ 1.8 MeV is possible for detection of explosive material
at customs control by nuclear resonance absorption of γrays in nitrogen.
Figure 2: Scheme of efficient accumulator-collider of
accelerated deuterium and tritium ions for neutron
generation in vacuum collisions of two merging beams.
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Proceedings of RuPAC XIX, Dubna 2004
Application for Mass Separation of Ions
Efficient mass-separator for separation of stable isotopes
of non volatile chemical elements in the weight amounts.
can be constricted on the basis ionic-cyclotron resonance
in the magnetic field of a superconducting solenoid. This
three- or four-stage mass-separator allows to select such
rare isotopes as 187,184 Os and 235 U from the depleted
uranium (from the waste of army uranium producing).
REFERENCES
[1] N.I. Tarantin, “Method of accelerating and strong
focusing of charged particles by constant electric field
and device for his realisation”. Patent 2212121 of
Russian Agency for Patents and Trade Marks.
Moscow, 10 September 2003. BIPÌ, 25, (2003), 613
(in Russian).
[2] N.I. Tarantin, III Scientific Seminar in Memory of
V.P. Sarantsev. Dubna, 22-23 September 1999. p. 180
(in Russian). Dubna D9-2000-69.
[3] N.I. Tarantin, IV Scientific Seminar in Memory of
V.P. Sarantsev. Dubna, 26-28 September 2001. p. 184
(in Russian). Dubna 2002.
[4] N.I. Tarantin, “New methods for considering and
calculating the ion-optical action of mass
spectrometers”. Intern. Journ. Mass Spectrometry and
Ion Phys. 46 (1983) 51.
[5] N.I. Tarantin, “Some aspect of the Penning trap
theory”. Nucl. Instr. Meth. B126 (1997) p.312.
[6] N.I. Tarantin, “A proposed storage ion trap of an “inflight capture” type for precise mass measurement of
radioiactive nuclear reaction products and fission
fragments”. Hyperfine Interactions 132 (2001) p. 443.
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