Polarized protons acceleration at U-70
A possibility to accelerate polarized proton at the synchrotron U-70 is considered. Estimations of the spin resonances are given in the energy range 2.5…70 GeV. To suppress depolarizing effects of spin resonances, a scheme of three partial Siberian snakes is suggested. Each snake consists from hel...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Zitieren: | Polarized protons acceleration at U-70 / A.V. Otboyev, P.Yu. Shatunov, Yu.M. Shatunov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 25-27. — Бібліогр.: 8 назв. — англ. |
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| author | Otboyev, A.V. Shatunov, P.Yu. Shatunov, Yu.M. |
| author_facet | Otboyev, A.V. Shatunov, P.Yu. Shatunov, Yu.M. |
| citation_txt | Polarized protons acceleration at U-70 / A.V. Otboyev, P.Yu. Shatunov, Yu.M. Shatunov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 25-27. — Бібліогр.: 8 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | A possibility to accelerate polarized proton at the synchrotron U-70 is considered. Estimations of the spin resonances
are given in the energy range 2.5…70 GeV. To suppress depolarizing effects of spin resonances, a scheme of
three partial Siberian snakes is suggested. Each snake consists from helical magnets with 4.5 T magnetic field. The
scheme provides the adiabatic spin flip at imperfection resonances and suppresses all intrinsic resonances by quite
realistic beam emittance and magnets misalignments ±5 mm.
В статье обсуждается возможность ускорения поляризованных протонов в синхротроне У-70. Дана оценка силы деполяризующих резонансов. Предлагается схема из трех спиральных частичных Сибирских змеек для подавления деполяризующего влияния, как целых, так и спибетатронных резонансов. Обсуждается конструкция спиральных магнитов и требования к качеству пучка и магнитной системы синхротрона У-70.
У статті обговорюється можливість прискорення поляризованих протонів у синхротроні У-70. Дана
оцінка сили деполяризуючих резонансів. Пропонується схема із трьох спіральних часткових Сибірських
змійок для придушення деполяризуючого впливу, як цілих, так і спин-бетатронних резонансів.
Обговорюється конструкція спіральних магнітів і вимоги до якості пучка і магнітної системи синхротрона
У-70.
|
| first_indexed | 2025-12-07T15:27:36Z |
| format | Article |
| fulltext |
POLARIZED PROTONS ACCELERATION AT U-70
A.V. Otboyev, P.Yu. Shatunov, Yu.M. Shatunov
Budker Institute of Nuclear Physics, Novosibirsk, Russia
E-mail:shatunov@inp.nsk.su
A possibility to accelerate polarized proton at the synchrotron U-70 is considered. Estimations of the spin reso-
nances are given in the energy range 2.5…70 GeV. To suppress depolarizing effects of spin resonances, a scheme of
three partial Siberian snakes is suggested. Each snake consists from helical magnets with 4.5 T magnetic field. The
scheme provides the adiabatic spin flip at imperfection resonances and suppresses all intrinsic resonances by quite
realistic beam emittance and magnets misalignments ±5 mm.
PACS: 29.17.+w
1. INTRODUCTION
At present moment there is a reach experience in an
acceleration of polarized protons in synchrotrons. But in
each concrete case one have to choose more appropriate
equipment and to solve problems how to implement
these parts in the existing machine lattice. First attempt
to consider this problem for U-70 have been done in
1984 year. However, proposed measures have demand-
ed big enough efforts to enlarge one straight section by
displacements of a number of dipole magnets.
First of all, let’s remind main approach to descrip-
tion of spin motion in accelerators. Quantum mechani-
cal average of spin operator ( )? ; ;x y zσ σ σ σ= − spin
vector S= ?ψ σ ψ∗ is moving in magnetic B and elec-
tric E fields along the generalized azimuth accelerator θ
according to the BMT equation: [1]
[ ]
[ ]0 0
;
,
1
S S W×S
W B B E×V
d
d
q qq
q q
θ
γ γ γ⊥
= =
ў ў− = + + + +
+
ў
ж ц ж ц
з ч з ч
и ш и ш
P
(1)
where magnetic field B is decomposed along particle
velocity V and transversely; q’, q0 are anomalous and
normal parts of the gyro-magnetic ratio q = q0 + q′.
Similar to the orbital motion a periodical part W0 of
the precession frequency (W=W0 + w) in (1) leads us to
a periodical solution – “spin closed orbit” n0 and spin
tune ν = W0/ω, [2] where
[ ]0 0
2 1
ω B E×Vq qγ
γ γ⊥− = +
−
(2)
is the Larmor frequency.
In usual case of a machine with the vertical guiding
field B=B⋅ez the spin precession axis n0 coincides with
the unit vector ez and spin tune in the accelerator frame
(ex;ey;ez) is equal to ν=γa=γq’/q0. Linear dependence of
the spin tune on particle energy creates many troubles
while acceleration, Multi periodical part w of the pre-
cession frequency is connected with particle deviations
from the CO due to some imperfections of magnetic
systems the same as betatron and synchrotron oscilla-
tions. How it’s seen from (1), first of all, radial magnet-
ic fields tilts n0 from the vertical direction. More danger-
ous situations happened when spin tune is equal to one
of a harmonic number of the radial field: ν =νk=k (k –
integer). In this case spin deflections are accumulated in
time. Finally, it can lead to a beam depolarization.
These imperfection spin resonances take place in each
440.652 MeV for electrons and 523.342 MeV for pro-
tons and their strengths increase with beam energy.
It’s clear, that resonances ν=k =P, where P is ma-
chine periodicity, are strongest between others. Thus for
acceleration of polarized particles one has to take a care
about a quality of the guiding magnetic field.
Moreover, due to the vertical betatron oscillations of
the particle its spin is deflected also by radial magnetic
fields, intrinsic for a beam focusing system (Bx~z). In
this case intrinsic spin resonances arise by a condition:
ν = νk = k ± νz ; (νz is vertical betatron tune). So, even in
the first linear approximation the acceleration of polar-
ized particles up to high energy looks very complicate
issue.
2. SPIN RESONANCE CROSSING
Let’s consider the case of a separate spin resonance
crossing. According to the paper [3] a change of polar-
ization is described by the formulae:
( )2 1f i iS S S S e χδ −= − = − , (3)
where 2 / 2kwχ π δ= & is a spin phase advance in a reso-
nance zone kwδ : : (wk − resonance strength; δ = ν - νk –
resonance tuning).
There are two practically interesting cases. By a fast
crossing ( 2
kwδ& ? ) the polarization change is small:
( 1).Sδ χ≈ = In opposite case slow (adiabatic)
tuning rate 2
kwδ& = we have a spin flip: f iS S−; with
exponentially small polarization losses. Based on this
understanding of the resonance passing process a num-
ber of practical approach have been developed for the
polarized particles acceleration. Compensations of CO
harmonics by correctors at imperfection resonances and
pulse quadrupoles at intrinsic are successfully applied
for the fast resonances crossing by the polarized proton
acceleration up to few GeV [4].
3. SIBERIAN SNAKES
Further progress required a different approach to the
resonance crossing. In 1976 it was suggested [5] to in-
troduce in machine lattice a special chain of magnets,
which will rotate spin by 180 degrees by pass. How it
easy to see, in this case the spin tune ν=1/2 indepen-
dently on the beam energy and the resonance condition
does not arise more totally. This approach was called as
Siberian snake. It can be arranged in different magnet
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.25-27.
25
combinations, which rotates spin around any axis. At
that the periodical precession axis n0 at opposite to the
snake azimuth lies in the horizontal plane with the same
angle to the CO as the snake axis.
The simplest snake is one solenoid with the longitu-
dinal integral field y zq B dl Bπ ρ=т ; (37 Tm for
10 GeV protons). Some disadvantage of the solenoidal
snake is a x-z coupling introduced by the longitudinal
field. There are a number of schemes with combinations
of solenoids and skew quads, that don’t excite the cou-
pling out side the insertion. But such schemes require,
as rule, a long straight section.
More compact partial snakes can be designed from
helical magnets /6/, because, how it’s seen from (1),
spin rotations by transverse fields don’t depend on ener-
gy for high energy particles whereas the action on spin
by longitudinal fields is inverse proportional to the ener-
gy. Orbit distortions from transverse fields can be mini-
mized in the case of helical magnets by a special snake
design a set of four full twist helixes with mirror sym-
metry and adjusted field levels. Such choice performs to
rotate spin by 180 degrees around an arbitrary direction
in the machine medium plane and compensate orbit dis-
tortions outside the snake taking them very moderate in-
side the insertion.
This advantage of helical snakes creates interesting
possibilities for high energy machines with combina-
tions of two Siberian snakes located at opposite az-
imuths with the snake axis perpendicular each other. In
this case n0 is vertical in arcs (n0 = ± ez) and spin tune
again is half integer (ν=1/2).
That is funny, that practically the same chain of heli-
cal magnets can work as spin rotator from vertical direc-
tion to horizontal plane.
The practical realization of these ideas have done at
RHIC, where are installed two pairs Siberian snakes in
each ring and eight spin rotators around two IP to deliv-
er the longitudinal polarization for two detector STAR
and PHENIX. Recently polarized protons in both rings
were accelerated up to top energy 205 GeV with rela-
tively small polarization losses.
4. PARTIAL SNAKE
But in the beginning so called a partial Siberian
snakes found practical applications. Such snake rotates
spin only by few degrees and thereby generates enough
strong artificial imperfection resonances, which satisfy to
the adiabatic condition. First test of this idea have been
done in 1976 year at electron-positron collider VEPP-2M
[6] and then routinely used to deliver e+e- beams, polar-
ized at the energy 700 MeV, to the energy below main
imperfection resonance ν=1 (E=440 MeV). Later the
solenoidal partial snake was applied at AGS, where po-
larized protons are accelerated up to 25 GeV with some
problems caused by mention above coupling [7].
Similar to full snakes the partial snakes from helical
magnets look more promising [8]. The strength of such
snake can be done big enough (up to 35% of the full
one; wk = 0.175). Partial snakes such strength or combi-
nations of few of them open a possibility to suppress
also intrinsic resonances. In a vicinity of each imperfec-
tion resonance ν=k there are two symmetric intrinsic
resonances (ν = k1 - νz and ν = k2 + νz). If these reso-
nances lie inside the zone of the imperfection one, spin
motion in such system is quite complicate, but computer
simulations show that under condition |wk1,2|=1/3|wk|
modulations of the precession axis due to this adjacent
resonances take adiabatic behavior and spin reverses in
the same way as on a single imperfection resonance.
5. SYNCHROTRON U-70
The proton synchrotron U-70 is operating in Protvi-
no since 1967 year. The synchrotron has 12 super-peri-
ods. The beam is injected from booster ring with
hjj
LINAC
BOOSTER
(+) ss (-) ss
(+) ss
Fig.1. Layout synchrotron U-70
the kinetic energy 1.5 GeV. The first attempt to modify
U-70 to polarized proton acceleration have been taken
yet at 1984./9/ However, proposed scheme have re-
quired big machine changes and it was not accepted.
The present proposal suggests install three identical par-
tial snakes in three super-periods of U-70, as it’s shown
in Fig.2. Each snake takes 3.5 m and consists of 4 peri-
ods helix (λ=70 cm; aperture 15 cm) with field up to 4.2
T. This combination rotates spin by 65 degrees. To
compensate some CO distortions two dipole coils are
wounded at the edges. Particle trajectories inside the
snake are shown in Fig.2 for the energy 25 GeV. Spin
rotation by the snake per pass is given in Fig.3. It’s
seen, that the snake axis is practically longitudinal and
spin map is σy.
Fig.2. Orbit inside the snake
Fig.3. Spin rotation inside the snake
26
x
z
Sx
Sz
Sy
The spin rotations by all identical polarities snakes
are added coherently at ν0 = k = m⋅P/4 (m are integers)
or at ν0 =k =(m+1/2)⋅P/4 with one snake polarity re-
verse. The last option is appeared more suitable for
U-70 (Fig.1).
A behavior the spin tune in this case is presented in
Fig.4 for the energy range of more strong spin reso-
nances. Their strengths |wk| are shown in the Fig.4 by tri-
angles and boxes for imperfection resonances and by
rounds for intrinsic resonances ν0 = νk = k⋅P ± νz. Estima-
tions of the |wk| have been done with assumptions:
dipoles vertical misalignments ±0.5 cm (in two different
ways); normalized vertical emittance don’t exceed 10-4⋅π
cm.
Fig.4. Spin tune with snakes and strongest resonances
Fig.5. Vertical polarization by acceleration
This figure visually demonstrates, that intrinsic reso-
nances are “absorbed” by imperfection resonances cre-
ated by the snakes combination.
It’s interesting to look at a motion of vertical compo-
nent of polarization while acceleration with the snakes
set (Fig.5).
Points with 100% vertical polarization are suitable
for polarized beam extraction.
6. CONCLUSIONS
Proposed schemes of three helical partial snakes at
U-70 can provide acceleration of polarized protons up to
top energy E=70 GeV under conditions a conservation
beam emittance from the booster ring during whole ac-
celeration cycle and alignment requirements for ma-
chine magnets ± 5 mm.
A manufacturing of the superconducting helical
magnet will demand some efforts. However, usual re-
quirements of field qualities are not crucial in this case,
because snakes take only short part of machine circum-
ference. Some optics distortion (<5%) can be easy cor-
rected by weak focusing coils at the edges of each
snake.
We didn’t discuss here possible problems with the
beam acceleration at the booster ring. But according to
international experience it can not be serious obstacle to
cross few weak spin resonances on low energy.
REFERENCES
1. V. Bargman, M. Michel, V. Telegdi // Phys. Rev.
Lett. 1959, v.2, p.435.
2. Ya. Derbenev, A. Kondratenko, A. Skrinsky // Sov.
Phys. Doklady. 1970, v.192, p.1255.
3. M. Froisart, R. Stora // Nucl. Instr. and Methods.
1960, v.7, p.297.
4. H. Huang et al. Proc. of the 13-th Int. Symposium
on High Energy Spin Phys. 1998, p.492.
5. Ya. Derbenev, A.Kondratenko // Part. Acc. .1978,
v.8, p.115.
6. V. Ptitsyn, Yu. Shatunov // Nucl. Instr. and Meth-
ods. 1997, v.A398, p.126
7. Ya. Derbenev et al. Proc. of the 10-th Int. Conf. On
High Energy Acc. 1977, v.2, p.272.
8. I. Koop et al. Proc. of PAC2003. 2003, p.2898.
УСКОРЕНИЕ ПОЛЯРИЗОВАННЫХ ПРОТОНОВ В У-70
А.В. Отбоев, П.Ю. Шатунов, Ю.М. Шатунов
В статье обсуждается возможность ускорения поляризованных протонов в синхротроне У-70. Дана оцен-
ка силы деполяризующих резонансов. Предлагается схема из трех спиральных частичных Сибирских змеек
для подавления деполяризующего влияния, как целых, так и спин-бетатронных резонансов. Обсуждается
конструкция спиральных магнитов и требования к качеству пучка и магнитной системы синхротрона У-70.
ПРИСКОРЕННЯ ПОЛЯРИЗОВАНИХ ПРОТОНІВ В У-70
А.В. Отбоєв, П.Ю. Шатунов, Ю.М. Шатунов
У статті обговорюється можливість прискорення поляризованих протонів у синхротроні У-70. Дана
оцінка сили деполяризуючих резонансів. Пропонується схема із трьох спіральних часткових Сибірських
змійок для придушення деполяризуючого впливу, як цілих, так і спин-бетатронних резонансів.
Обговорюється конструкція спіральних магнітів і вимоги до якості пучка і магнітної системи синхротрона
У-70.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.25-27.
27
Ускорение поляризованных протонов в У-70
ПРИСКОРЕННЯ ПОЛЯРИЗОВАНИХ ПРОТОНІВ В У-70
|
| id | nasplib_isofts_kiev_ua-123456789-78939 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:27:36Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Otboyev, A.V. Shatunov, P.Yu. Shatunov, Yu.M. 2015-03-24T07:33:35Z 2015-03-24T07:33:35Z 2006 Polarized protons acceleration at U-70 / A.V. Otboyev, P.Yu. Shatunov, Yu.M. Shatunov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 25-27. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 29.17.+w https://nasplib.isofts.kiev.ua/handle/123456789/78939 A possibility to accelerate polarized proton at the synchrotron U-70 is considered. Estimations of the spin resonances are given in the energy range 2.5…70 GeV. To suppress depolarizing effects of spin resonances, a scheme of three partial Siberian snakes is suggested. Each snake consists from helical magnets with 4.5 T magnetic field. The scheme provides the adiabatic spin flip at imperfection resonances and suppresses all intrinsic resonances by quite realistic beam emittance and magnets misalignments ±5 mm. В статье обсуждается возможность ускорения поляризованных протонов в синхротроне У-70. Дана оценка силы деполяризующих резонансов. Предлагается схема из трех спиральных частичных Сибирских змеек для подавления деполяризующего влияния, как целых, так и спибетатронных резонансов. Обсуждается конструкция спиральных магнитов и требования к качеству пучка и магнитной системы синхротрона У-70. У статті обговорюється можливість прискорення поляризованих протонів у синхротроні У-70. Дана оцінка сили деполяризуючих резонансів. Пропонується схема із трьох спіральних часткових Сибірських змійок для придушення деполяризуючого впливу, як цілих, так і спин-бетатронних резонансів. Обговорюється конструкція спіральних магнітів і вимоги до якості пучка і магнітної системи синхротрона У-70. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ускорители заряженных частиц Polarized protons acceleration at U-70 Ускорение поляризованных протонов в У-70 Прискорення поляризованих протонів в У-70 Article published earlier |
| spellingShingle | Polarized protons acceleration at U-70 Otboyev, A.V. Shatunov, P.Yu. Shatunov, Yu.M. Ускорители заряженных частиц |
| title | Polarized protons acceleration at U-70 |
| title_alt | Ускорение поляризованных протонов в У-70 Прискорення поляризованих протонів в У-70 |
| title_full | Polarized protons acceleration at U-70 |
| title_fullStr | Polarized protons acceleration at U-70 |
| title_full_unstemmed | Polarized protons acceleration at U-70 |
| title_short | Polarized protons acceleration at U-70 |
| title_sort | polarized protons acceleration at u-70 |
| topic | Ускорители заряженных частиц |
| topic_facet | Ускорители заряженных частиц |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78939 |
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