Ion beam forming dynamics in an injector taking into account a plasma boundary
The developed program code taking into account a shape and position of an emitting plasma boundary had been used to examine a deuterium beam forming in an injector. It has been shown that the beams formed by a three-electrode ion optical system have a complex density distribution in a beam phase spa...
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irk-123456789-792602015-03-31T03:02:13Z Ion beam forming dynamics in an injector taking into account a plasma boundary Demchenko, P.O. Shulika, M.G. The developed program code taking into account a shape and position of an emitting plasma boundary had been used to examine a deuterium beam forming in an injector. It has been shown that the beams formed by a three-electrode ion optical system have a complex density distribution in a beam phase space. For the narrow current range it is possible to have a beam crossover at the injector output with a radius of 1mm and divergence less then 20 mrad. 2001 Article Ion beam forming dynamics in an injector taking into account a plasma boundary / P.O. Demchenko, M.G. Shulika // Вопросы атомной науки и техники. — 2001. — № 3. — С. 144-146. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS numbers: 29.20.Bd http://dspace.nbuv.gov.ua/handle/123456789/79260 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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The developed program code taking into account a shape and position of an emitting plasma boundary had been used to examine a deuterium beam forming in an injector. It has been shown that the beams formed by a three-electrode ion optical system have a complex density distribution in a beam phase space. For the narrow current range it is possible to have a beam crossover at the injector output with a radius of 1mm and divergence less then 20 mrad. |
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Article |
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Demchenko, P.O. Shulika, M.G. |
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Demchenko, P.O. Shulika, M.G. Ion beam forming dynamics in an injector taking into account a plasma boundary Вопросы атомной науки и техники |
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Demchenko, P.O. Shulika, M.G. |
| author_sort |
Demchenko, P.O. |
| title |
Ion beam forming dynamics in an injector taking into account a plasma boundary |
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Ion beam forming dynamics in an injector taking into account a plasma boundary |
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Ion beam forming dynamics in an injector taking into account a plasma boundary |
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Ion beam forming dynamics in an injector taking into account a plasma boundary |
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Ion beam forming dynamics in an injector taking into account a plasma boundary |
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ion beam forming dynamics in an injector taking into account a plasma boundary |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2001 |
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http://dspace.nbuv.gov.ua/handle/123456789/79260 |
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Ion beam forming dynamics in an injector taking into account a plasma boundary / P.O. Demchenko, M.G. Shulika // Вопросы атомной науки и техники. — 2001. — № 3. — С. 144-146. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT demchenkopo ionbeamformingdynamicsinaninjectortakingintoaccountaplasmaboundary AT shulikamg ionbeamformingdynamicsinaninjectortakingintoaccountaplasmaboundary |
| first_indexed |
2025-07-06T03:18:06Z |
| last_indexed |
2025-07-06T03:18:06Z |
| _version_ |
1836865958471270400 |
| fulltext |
ION BEAM FORMING DYNAMICS IN AN INJECTOR TAKING INTO
ACCOUNT A PLASMA BOUNDARY
P.O. Demchenko, M.G. Shulika
Institute of Plasma Electronics and New Methods of Acceleration,
National Scientific Center "Kharkov Institute of Physics and Technology"
Kharkov, Ukraine, demchenko@kipt.kharkov.ua
The developed program code taking into account a shape and position of an emitting plasma boundary had been
used to examine a deuterium beam forming in an injector. It has been shown that the beams formed by a three-elec-
trode ion optical system have a complex density distribution in a beam phase space. For the narrow current range it
is possible to have a beam crossover at the injector output with a radius of 1mm and divergence less then 20 mrad.
PACS numbers: 29.20.Bd
1 INTRODUCTION
Now in the world some proton and deuteron linacs
up to energy 1-1.5 GeV and an average beam current of
5÷100 mA are being developed [1]. These accelerators
are intended for production of high neutron flows or for
tritium production. For realization of these accelerators
the high current injectors are needed with a high beam
luminosity. In all designs it is supposed the injection of
ion beams with the energy 50÷100 keV in an initial part
of the accelerator on the basis of a radio-frequency
quadrupole focusing (RFQ). That imposes some re-
quirements on a value and shape of the beam phase vol-
ume at an RFQ input.
The requirements to the ion optical performances of
the injected beams have stimulated the mathematical
modeling of ion beam forming from the plasma of gas
discharge sources. One of the modeling problems is the
definition of the shape and location of a self-consistent
plasma boundary, from which ions are extracted, and
initial conditions for starting particles. In the present
work for examination of ion beam forming dynamics
from plasma with the help of three-electrode ion optical
system the code INJECTOR was used [2]. The code
takes into account a location and shape of an emitting
plasma boundary. The results of the numerical modeling
are given for a deuterium beam with the output energy
100 keV. The beam is intended for injection to a
deuteron linac with the output energy 10÷12 MeV for
production of a medicine isotope-generator 99Mo as a re-
sult of a nuclear reaction 98Mo(d,p)99Mo [3].
2 THE PROGRAM CODE FOR SIMULA-
TION OF ION BEAM FORMING
The description of the INJECTOR code is given in
[2]. The code is based on the solution of a motion prob-
lem for ions, emitted from a plasma boundary, in a self-
consistent electric field produced by forming system
electrodes with given potentials and a beam space
charge. The emitting plasma boundary is supposed
smooth and crossing an aperture in a plasma electrode 1,
Fig. 1, which is contacting with plasma.
The shape of the boundary was supposed to be a sur-
face of revolution of the second degree curve (spherical,
elliptic or parabolic segment). In zero approach a plas-
ma boundary position (a zb point of crossing with a lon-
gitudinal z-axis) was defined from the balance of a ki-
netic plasma momentum and momentum of a vacuum
electric field produced by injector electrodes: nkTe=ε
oE2/2, where n is the plasma density, Te is the electron
temperature, E is the electric field strength, k is the
Boltzmann constant, ε0 is the dielectric constant of vac-
uum.
Fig. 1. Deuteron trajectories for the beam current
I=40mA.
Since the initial parameters of the problem are sup-
posed: a beam current I, electron Te and ion Ti tempera-
tures, the plasma density was determined from the ex-
pression for an ion saturation current: I=0.4Zen
(2kTe/M) 1/2S [4], where Ze and M are the charge and the
mass of an ion, respectively, S is the area of an emitting
plasma surface.
The plasma boundary potential was guessed equal to
the plasma electrode potential. The potential jump in a
double layer was taken into account in the start ion ve-
locity. I.e. it was supposed, that ions are starting along a
normal line to the plasma surface with a velocity
vo=(kTe/M)1/2, defined by the Bohm criterion [4].
The ion velocity component, tangential to plasma
surface, was defined by the ion temperature Ti and was
(kTi/M)1/2. Knowledge of the plasma boundary and the
initial velocities of ions allows to calculate their trajec-
tory in an injector ion optical system and respectively a
space charge distribution ρ(r,z). For the calculation of
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №3.
Серия: Ядерно-физические исследования (38), с. 144-146.
144
mailto:demchenko@kipt.kharkov.ua
the space charge the method of macroparticles was used
[5].
Fig. 2. Deuteron trajectories for the beam current
I=90 mA.
For successive iterations of the electric field deter-
mination the Poisson equation was solved using a new
space charge distribution. Every time the position of the
plasma boundary was defined more exactly using the re-
quirement that the electric field strength would be ap-
proximately zero in a point zb where the boundary was
crossed by z-axis. During the simulation the minimum
boundary field strength was taken kTe/ehz, where hz is a
step along z-direction of a computing grid, e is elemen-
tary charge.
This process had been repeated until the converging
solution had been succeeded.
3 RESULTS OF DEUTERON BEAM FORM-
ING SIMULATION
The INJECTOR program code was used to simulate
the forming process for a deuterium beam with the ener-
gy 100 keV. The ion optical system with an accel-deccel
potential difference between electrodes was considered.
The respective ion injector is supposed to use for beam
injection in RFQ of a deuteron linac of energy 10÷
12MeV for production of a medicine isotope-generator
99Mo. This radionuclide may be produced due to a nu-
clear reaction 98Mo(d,p)99Mo under bombardment by
deuterons of a target from a natural molybdenum or one
enriched by a natural isotope 98Mo [3].
The electron Te and ion Ti plasma temperatures were
chosen Te=5eV and Ti=1eV, respectively, as the most
probable for many gas discharge plasma sources [6].
The geometry of the injector forming system is shown
in Fig. 1.
The plasma electrode 1, Fig. 1, directly contacting
with the gas discharge plasma, had potential U1=100 kV
relative to a grounded electrode 3. Radius of the input
aperture in the plasma electrode 1 was ro=0.4 cm. A po-
tential of an extraction electrode 2, Fig. 1, was
U2 = -10 kV. A length of an extraction gap between
electrodes 1 and 2, Fig. 1, was d=2 cm. i. e. the length d
was above the minimum value causing a vacuum break
down: d≥1.4⋅10-3U3/2, where d is in cm, U=U1-U2 is in
kV [6].
In Fig. 1 and Fig. 2, the trajectories of deuterons are
shown for two values of a total beam current I or ac-
cordingly for different plasma densities n. In Fig. 3 and
Fig. 4 the respective distributions of particle density in a
transverse phase plane of the formed beams are given.
Fig. 3. Density distribution in a transverse plane of
the beam phase space for I=40 mA.
Here in Fig. 3 and Fig. 4 the root mean square values
(rms) of a beam width Xrms and its divergence X'rms at
an injector output are indicated and also scales Xm and
X'm of the respective coordinate axes.
Fig. 4. Density distribution in a transverse plane of
the beam phase space for I=90 mA.
As well as in case of a proton beam in ref. [2], for a
deuteron beam there are three modes of its forming, de-
pending on a total beam current I or according to plasma
density n. At small currents I with regard to the Child-
Langmuir value Ich=(4/9) (Ze/M)1/2εoU3/2S/d2, the diver-
gent beams are formed with a crossover in the extrac-
tion gap and a concave emitting boundary of plasma,
Fig. 5, I=10 mA.
With increase of the beam current the crossover dis-
places to the injector output. At some current value
I=Iopt, in this case Iopt≈40÷50 mA, at the injector output,
Fig. 1, the minimum beam width, is produced, Fig. 3.
The beam radius does not exceed 1mm. Thus the nor-
malized emittance is εn=2⋅10-2 π⋅cm⋅mrad. Simultane-
ously the emitting plasma boundary approaches to flat
in limits of the plasma electrode aperture, Fig. 5,
145
I=40 mA.
At I>Iopt the plasma boundary becomes convex to
the extraction gap, Fig. 5, I=90 mA, and the formed
beams are strongly divergent and have no crossover,
Fig. 2 and Fig. 4.
Fig. 5. Shape of the plasma boundary versus a beam
current.
Fig. 6. Spherical (1) and elliptical (2) shapes of the
plasma boundary for the beam current I=90 mA.
It is necessary to note that with the help of the
smooth second-order curves it is impossible to obtain
the solution with the constant electric field strength
along the plasma boundary.
The results of modeling have given an oscillating
character of the field strength. At currents of a formed
beam of about I≈Ich the minimum field oscillations and
also the higher convergence rate of the solution are ob-
served when the plasma boundary has an ellipsoid form
with the relation of a vertical semi-axis to the longitudi-
nal one of order 4, curve 2, Fig. 6.
4 CONCLUSION
The results of the mathematical simulation indicate
that the chosen ion optical system allows to produce a
deuterium beam with a radius no more than 1 mm and
divergence less then 20 mrad at an injector output, but
in a very narrow interval of a beam current of 40÷
50 mA at a deuteron energy 100 keV. It is obviously pos-
sible to calculate a RFQ section, which will transport
such a beam without a matching unit. At other currents
of a beam or its ion optical performances, a matching
unit, for example similar LEBT (Low Energy Beam
Transport) used in [7], is needed. The nonlinear effects
caused by a vacuum electric field, and a space charge
field of a high current beam, are resulting in a complex
particle density distribution in a beam phase space and
are increasing a beam effective emittance.
REFERENCES
1. I.D.Schneider. Overview of High Power CW Pro-
ton Accelerators // Proceedings of EPAC 2000, Vi-
enna, Austria, 2000, p. 118-121.
2. P.O.Demchenko, M.G.Shulika. A Simulation Code
to Model an Ion Beam Forming in an Injector //
Proc. of the Seventh European Particle Accelerator
Conference, Vienna, Austria, 2000, p. 1363-1365.
3. P.O.Demchenko, V.A.Voronko, V.Ya.Migalenja
and et al. Application of compact linacs for the
medical purposes // Problems of Atomic Science
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5. D.Potter. Computational Physics. New York: John
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6. G.Bolme, L.Hansborough, T.Hardek, et al. Half-
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