Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Cite this: | Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis / I.A. Vorobyov, D.A. Liakin // Вопросы атомной науки и техники. — 2001. — № 3. — С. 158-160. — Бібліогр.: 11 назв. — англ. |
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Vorobyov, I.A. Liakin, D.A. 2015-03-30T08:27:08Z 2015-03-30T08:27:08Z 2001 Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis / I.A. Vorobyov, D.A. Liakin // Вопросы атомной науки и техники. — 2001. — № 3. — С. 158-160. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS nambers: 29.20.Bd https://nasplib.isofts.kiev.ua/handle/123456789/79266 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis Динамика пучка в линейном ускорителе на высокие энергии с помощью метода полувариантов и анализа скоплений Article published earlier |
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Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis |
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Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis Vorobyov, I.A. Liakin, D.A. |
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Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis |
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Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis |
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Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis |
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Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis |
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beam dynamics issue in high power linac with the use of method of semiinvariants and cluster analysis |
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Vorobyov, I.A. Liakin, D.A. |
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Vorobyov, I.A. Liakin, D.A. |
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2001 |
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English |
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Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Динамика пучка в линейном ускорителе на высокие энергии с помощью метода полувариантов и анализа скоплений |
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1562-6016 |
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Beam dynamics issue in high power LINAC with the use of method of semiinvariants and cluster analysis / I.A. Vorobyov, D.A. Liakin // Вопросы атомной науки и техники. — 2001. — № 3. — С. 158-160. — Бібліогр.: 11 назв. — англ. |
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BEAM DYNAMICS ISSUE IN HIGH POWER LINAC WITH THE USE OF
METHOD OF SEMIINVARIANTS AND CLUSTER ANALYSIS
I.A. Vorobyov, D.A. Liakin
Institute of Theoretical and Experimental Physics
117259 B.Cheryomushkinskaya, 25, Moscow, Russia, ITEP
E-mail vorobjev@vitep5.itep.ru
PACS numbers: 29.20.Bd
For the beam dynamics issue in the ITEP structural
scheme of the high power Linac [1, 2] a necessity in de-
velopment of methods of beam dynamics analysis,
which are sensitive to the space charge redistribution
and able to reveal particularities in halo formation at all
stages of acceleration, is appeared1.
Development of semiinvariants method began in
1995 year, results obtained were presented at first at
XVI Workshop on charged particle accelerators in
Alushta in 1997 [3]. The method has a high sensitivity
to space charge redistribution in a phase space and a
convenient property for comparison with the Gauss dis-
tribution. For the Gauss distribution all semiinvariants
from the third order are equal to zero. Following investi-
gations of charged particle dynamics for initial trans-
verse KV distribution with the use of this method re-
vealed three stages in space charge evolution and stabil-
ity conditions of simulation results according to the
number of macroparticles [4, 5]. Calculations were
made with the use of a PROTON code [6, 7].
Dependences of the RMS normalized beam emit-
tance at the end of RFQ [8] with an initial emittance of
0.2 cmmrad and a semiinvariant of six order at its be-
ginning on the number of macroparticles are shown in
Fig. 1. As is seen from this figure the stability region
begins from 3000 macroparticles. Dependences of semi-
invariants on the RFQ cell for 1000 and 10000
macroparticles have the same character as in Fig. 3.
Fig. 1. Dependences of RMS normalized emittances at
the RFQ exit and initial (at the beginning of RFQ)
semiinvariant of six order in transverse planes for KV
distribution on the number of macroparticles for the
injected beam current 150 mA.
1 Development of Linac structural scheme was made un-
der ISTC project No.17.
Beam dynamics simulation in the whole ITEP struc-
tural scheme of Linac is made without proper matching
at crossing between the initial, intermediate and main s.
The following main parameters are accepted in calcula-
tions: the initial part with the RFQ structure at 150 MHz
to the end energy 3 MeV, the intermediate part with the
Alvaretz structure at 300 MHz to the end energy
100 MeV and the main part with the single gap res-
onators at 600 MHz to the end energy 1.5 GeV. Phase
advance in the main part is equal to 1.0 at the whole
length. Calculation was made for an injected beam cur-
rent of 30 mA with the initial emittance 0.2 cmmrad and
the matched initial uniform transverse distribution of
charged particles with the energy spread ±1%. In the nu-
merical simulation 5000 macroparticles were used.
Data obtained were analyzed with the use of the
method of semiinvariants. The results are shown in
Fig. 2 for the Linac and in Fig. 3 for the initial part with
the RFQ structure.
Fig. 2. Dependences of access coefficients γ2 and semi-
invariant χ6/χ2
3 on the time of acceleration in the Linac.
Fig. 3. Dependences of asymmetry and access coeffi-
cients on the RFQ cell number.
The results obtained in investigations of beam dy-
namics with a uniform initial distribution confirm the
earlier conclusion for the KV distribution [4, 5] about
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №3.
Серия: Ядерно-физические исследования (38), с. 158-160.
158
mailto:vorobjev@vitep5.itep.ru
tree stages of space charge evolution: 1) stage of fast re-
laxation, 2) stage of relative stabilization of charged
particle distribution, 3) stage of distribution destabiliza-
tion and beam halo formation. Also, the results confirm
the tendency in space charge evolution to the Gauss dis-
tribution revealed in the initial part.
The requirement for development of the method of
semiinvariants was a possibility of its application to ex-
perimental data analyzing. The measurements of beam
proton distribution on the phase plane were made at the
RFQ structure [9] of the ITEP “Istra” accelerator with
the use of measurement installation [10]. This method
allows to make measurements at one pulse of accelera-
tor work, that significantly accelerate the process of dif-
ferent characteristics and dependences removal. The ba-
sic principle of measurements is selecting the beam par-
ticles, located in small regions, which have fixed coordi-
nates in perpendicular to the accelerating axe planes.
After some drift space the selected particles, which have
initially a δ-space distribution, redistribute according to
the transverse component of their motion. Measuring a
brightness of luminosity scintillating under influence of
crossing through it particle screen, it is possible to ob-
tain information about phase distribution of beam. In
these measurements for selecting particles with fixed
coordinates an immovable wolfram screen with a net
step of 2.5 mm and hole diameter of 0.1 mm was used.
Drift of 110 mm allowed to obtain the angle separation
1 mrad. Measurement data processing was made with
the use of the method of semiinvariants developed in
[3-5], the results are shown in Fig. 4 and Table 1.
As it is seen from Table 1 and Fig. 3, the range of
measured values of asymmetry γ1 and access γ2 coeffi-
cients is well agreed with data of numerical simulation
with the use of the PROTON code, which was applied
for designing the RFQ structure [8, 9].
a b
Fig. 4. Measured phase portraits of the beam for a
beam current of 20 mA in horizontal (a) and vertical
(b) planes at the RFQ exit. In 4b, for comparison
with the canonical shape, the ellipse is shown.
Table 1. Experimental values of asymmetry and
access coefficients for the beam at the exit of
RFQ
Pa-
rame-
ter
Plane
Horiz. Vert.
γ1 -0,26 0,132
γ2 0,4 -0,74
Method of semiinvariants begins to extend in
physics of charged particle beams [11], that confirms
actuality of development of such a method.
For revealing specific conditions of halo formation
in each constructive part of the Linac the method of
cluster analysis of beam dynamics in radial and longitu-
dinal phase planes was developed. This method revealed
coupling of longitudinal and transverse motions .for ini-
tial KV distribution, made dependent by the resonance
of the third order [5].
For continuous run of a beam in the Linac with ini-
tially uniform transverse particle distribution, the
Poincare surfaces for all particles in radial and longitu-
dinal phase planes are shown in Fig. 5 at last 50 focus-
ing periods of the main part. For the radial surface we
determined the radius value 1.0 cm to select a halo par-
ticle group. The selected at the whole length, main part
group of particles with maximal deviation from the
channel axe above this radius consists from 341 parti-
cles. The results of cluster analysis for these particles
are shown in Fig. 6 – Fig. 9.
Fig. 5. Radial and longitudinal Poincare surfaces at
last 50 focusing periods of the main part of the Linac
for all particles.
Fig. 6. Radial and longitudinal phase portraits at the
beginning of the RFQ electrodes for the halo group.
Fig. 7. Radial and longitudinal phase portraits at the
end of the RFQ electrodes for halo group.
Fig. 8. Radial and longitudinal phase portraits at the
end of the intermediate part for the halo group.
159
Fig. 9. Radial and longitudinal phase portraits at the
end of the main part for the halo group.
As it is seen from Fig. 6 – Fig. 9, particles of halo
group, having no significant particularities in longitudi-
nal distribution while injecting the monochromatic
beam, move mainly in the peripheral region of longitu-
dinal phase portrait of bunch to the end of RFQ and in
the end of intermediate part redistribute in the periphery
of radial one. In the main part picture of halo particle
group dynamics is maintained in the both phase planes
while carrying out particles to large distances from the
channel axe and redistributing to the center of separa-
trix.
CONCLUSION
The methods of semiinvariants and cluster analysis
developed allow to reveal the processes, leading to car-
rying out the part of particles into halo and tendencies in
evolution of charged particles distribution, determine
the parameters of nonstationary processes, make physi-
cally and mathematically well-founded conclusion
about possibility of using the beam stationary model in
calculations, obtain the necessary data for choice of a
parametric family of functions.
The methods developed have revealed coupling of
transverse and longitudinal particle oscillations, objec-
tive laws in halo particles dynamics and specific partic-
ularities of halo formation in each constructive part of
the Linac. This allows to optimize the structural scheme
with taking into account the objective laws in the beam
dynamics and halo particle group and to calculate the
effective system of halo scrapping.
Applying the method of semiinvariants for experi-
mental data analyzing at the end of the RFQ structure
showed a good agreement with simulation results with
the use of the PROTON code.
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