Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells
An array of short sections of plasma dielectric wakefield accelerator modules spaced by vacuum zones (without plasma) is proposed to avoid the “underdense” operating regime. A calculation of the dynamics of the accelerated particles in such an array of accelerating-drift sections is given. The param...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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irk-123456789-1123602017-01-21T03:02:42Z Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells Kniaziev, R.R. Marshall, T.C. Sotnikov, G.V. Новые и нестандартные ускорительные технологии An array of short sections of plasma dielectric wakefield accelerator modules spaced by vacuum zones (without plasma) is proposed to avoid the “underdense” operating regime. A calculation of the dynamics of the accelerated particles in such an array of accelerating-drift sections is given. The parameters of bunches which are available in SLAC are used for this calculation. A dielectric structure using fused silica provides an operating frequency ~ 350 GHz. Lengths of plasma and vacuum sections providing stable transportation of the accelerated bunch are found. The bunch size in the focal plane is determined. Пропонується використовувати масив відносно коротких секцій плазмово-діелектричних кільватерних прискорювальних (ПДКП) модулів, розділених вакуумними проміжками (без плазми, хоча вони можуть містити діелектричну структуру), з метою уникнути небажаного перефокусування згустку, що прискорюється. Проведено розрахунок динаміки частинок, що прискорюються, у такій решітці прискорювально-дрейфових секцій ПДКП. Для розрахунків використані параметри згустків, наявні в SLAC. Діелектрична структура на основі плавленого кварцу забезпечує робочу частоту ~ 350 ГГц. Знайдено довжини плазмової й вакуумної секцій, які забезпечують стійке транспортування згустку, що прискорюється. Визначені розміри згустку у фокальній площині. Предлагается использовать массив относительно коротких секций плазменно-диэлектрических кильватерных ускорительных (ПДКУ) модулей, разделенных вакуумными промежутками (без плазмы, хотя они могут содержать диэлектрическую структуру), с целью избежать нежелательной перефокусировки ускоряемого сгустка. Проведен расчет динамики ускоряемых частиц в такой решетке ускорительно-дрейфовых секций ПДКУ. Для расчета использованы параметры сгустков, имеющиеся в SLAC. Диэлектрическая структура на основе плавленого кварца обеспечивает рабочую частоту ~ 350 ГГц. Найдены длины плазменной и вакуумной секций, обеспечивающих устойчивую транспортировку ускоряемого сгустка. Определены размеры сгустка в фокальной плоскости. 2015 Article Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells / R.R. Kniaziev, T.C. Marshall, G.V. Sotnikov // Вопросы атомной науки и техники. — 2015. — № 6. — С. 42-46. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 41.75.Ht, 41.75.Lx, 41.75.Jv, 96.50.Pw, 533.9. http://dspace.nbuv.gov.ua/handle/123456789/112360 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии |
| spellingShingle |
Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии Kniaziev, R.R. Marshall, T.C. Sotnikov, G.V. Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells Вопросы атомной науки и техники |
| description |
An array of short sections of plasma dielectric wakefield accelerator modules spaced by vacuum zones (without plasma) is proposed to avoid the “underdense” operating regime. A calculation of the dynamics of the accelerated particles in such an array of accelerating-drift sections is given. The parameters of bunches which are available in SLAC are used for this calculation. A dielectric structure using fused silica provides an operating frequency ~ 350 GHz. Lengths of plasma and vacuum sections providing stable transportation of the accelerated bunch are found. The bunch size in the focal plane is determined. |
| format |
Article |
| author |
Kniaziev, R.R. Marshall, T.C. Sotnikov, G.V. |
| author_facet |
Kniaziev, R.R. Marshall, T.C. Sotnikov, G.V. |
| author_sort |
Kniaziev, R.R. |
| title |
Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells |
| title_short |
Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells |
| title_full |
Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells |
| title_fullStr |
Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells |
| title_full_unstemmed |
Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells |
| title_sort |
transport of bunches in a dielectric wakefield accelerator using an array of plasma cells |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Новые и нестандартные ускорительные технологии |
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http://dspace.nbuv.gov.ua/handle/123456789/112360 |
| citation_txt |
Transport of bunches in a dielectric wakefield accelerator using an array of plasma cells / R.R. Kniaziev, T.C. Marshall, G.V. Sotnikov // Вопросы атомной науки и техники. — 2015. — № 6. — С. 42-46. — Бібліогр.: 8 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-08T03:48:11Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №6(100) 42
TRANSPORT OF BUNCHES IN A DIELECTRIC WAKEFIELD
ACCELERATOR USING AN ARRAY OF PLASMA CELLS
R.R. Kniaziev1, T.C. Marshall2, G.V. Sotnikov1
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2Columbia University, New York City, USA
E-mail: sotnikov@kipt.kharkov.ua
An array of short sections of plasma dielectric wakefield accelerator modules spaced by vacuum zones (without
plasma) is proposed to avoid the “underdense” operating regime. A calculation of the dynamics of the accelerated
particles in such an array of accelerating-drift sections is given. The parameters of bunches which are available in
SLAC are used for this calculation. A dielectric structure using fused silica provides an operating frequency
~ 350 GHz. Lengths of plasma and vacuum sections providing stable transportation of the accelerated bunch are
found. The bunch size in the focal plane is determined.
PACS: 41.75.Ht, 41.75.Lx, 41.75.Jv, 96.50.Pw, 533.9.
INTRODUCTION
Recent interest in dielectric wakefield accelerator
physics directed toward an advanced high-gradient accel-
erator [1] has been rekindled by the finding that certain
dielectrics can withstand very high fields (>1 GV/m) for
the short times involved in the passage of charged bunch-
es along a dielectric-lined channel [2]. A cylindrical, sin-
gle-channel dielectric-lined structure has been shown to
be an attractive and simple symmetric structure for high
gradient acceleration of electron or positron bunches
[3]. However, two problems have stood in the way of
the implementation of this concept: first, the bunch mo-
tion is afflicted with instabilities (see [4] and references
therein), and second, the transformer ratio is only ~ 2
[5]. Stabilizing the instabilities using external focusing
is challenging in a small structure as required for high
gradient acceleration. Also, while a ramped-charge drive
bunch or train of bunches has been shown to increase
the transformer ratio [6], such a bunch train may suffer
unstable motion. One cure that has been suggested for
these difficulties is the coaxial DWA, where the intro-
duction of an inner coaxial dielectric tube has been
shown [7] to offer better stability and elevated trans-
former ratio. Nevertheless, the complication of center-
ing and suspending the inner tubing of the coax in a
lengthy accelerator structure can be challenging.
Recently we have proposed to revisit the single
channel configuration through which both the collinear
drive and witness bunches move, but now fill this single
channel with plasma [8] – plasma-dielectric wakefield
accelerator (PDWA). We have found that the plasma can
provide an important radial focusing force on the wit-
ness bunch; this might secure the advantage of higher
transformer ratio using drive bunch ramping without the
penalty of unstable bunch motion, in an axially-
symmetric, smooth-bore, one-channel structure.
Plasma filling the transport channel of DWA oper-
ates similar to a plasma lens. In a lengthy unit this fo-
cusing could lead eventually to over-compression of the
bunch, in which case the bunch density will exceed the
plasma density and the undesirable “blowout” regime
obtains. Besides, it is very hard to create plasma and
sustain this homogeneity on a long distance. Thus a
PDWA will inevitably consist of plasma cells with gaps
between them. Therefore, for a bunch transport, we pro-
pose the use of a series of relatively short focusing
PDWA units that are spaced by vacuum zones so that
the ''focal point'' (minimum bunch radius) would lie in a
vacuum space. Our requirement is only that these vac-
uum spaces not be filled with plasma − they could still
be accelerator units, e.g. vacuum dielectric wakefield
accelerator sections, that maintain the acceleration gra-
dient but do not supply a strong radial force. The results
of a study of the dynamics of the accelerated particles in
such an array of accelerating-drift sections are presented
in this paper.
STATEMENT OF THE PROBLEM
The principal scheme of the proposed accelerator
based on plasma-dielectric modules is given in Fig. 1
which presents two PDWA cells separated by a vacuum
space. Each PDWA cell is a section of cylindrical di-
electric waveguide filled with plasma [8]; the gap be-
tween them (drift space) is the vacuum section of the
same waveguide. The length of the first cell is 1pL , the
length of the second cell is 2pL , the gap length is sL .
Fig. 1. Schematic of a pair of PDWA units used
as focusing elements to transport a bunch of test
particles that are located at the witness bunch
A drive bunch travelling through the accelerating sys-
tem excites in each PDWA cell a wakefield [8] which
accelerates the particles of a witness bunch. In the vac-
uum gap any forces acting on the witness bunch parti-
cles are absent.
A dynamics of witness bunch particles are described
by relativistic motion equations:
( , ) ( , ) ,z r
z
z
du
E r H r
dz
uq
cmu φψ
γ
γ ψ⎡ ⎤
= +⎢ ⎥
⎣ ⎦
( , ) ( , ) ,r z
r
z
du q E r H r
u
mudz c φ
γ ψ ψ
γ
⎡ ⎤
= −⎢ ⎥
⎣ ⎦
( )1/22 2, 1, 1d
r z
r
z z
u
u u
u u
vdr d
dz dz
ψ γ
γ = += − += , (1)
ISSN 1562-6016. ВАНТ. 2015. №6(100) 43
where ( )dv t z zψ = − , q and m are the electron charge
and mass, dv is the longitudinal velocity of the drive
bunch. If a certain witness bunch electron (“test” parti-
cle) is inside the drift space 1 2p pL z L< < then electro-
magnetic field components acting on it is equal 0:
0,z rE E Hφ= = = (2)
or else they can be presented in a sum of two items:
, ,L d L d d
z z z r r rE E E E E E H Hϕ ϕ= + = + = . (3)
In eq. (3) ,L L
z rE E are components of electric field of
Langmuir wave, and , ,d d d
rzE E Hϕ are components of
the electric and magnetic fields of the dielectric wave.
Explicit form of all components of the wakefield is giv-
en in ref. [8].
DYNAMICS OF TEST PARTICLES
For numerical calculation of the components of the
wakefield (2), (3) which accelerates the witness bunch
electrons we used parameters of electron bunches acces-
sible at SLAC: the energy of drive bunch electrons was
3 GeV, the bunch charge was 3 nC, its length was
0.2bL = mm, the drive bunch radius was
0.45br = mm. The PDWA cell is a section of a cylin-
drical dielectric waveguide with an outer radius of the
quartz tube ( 3.75ε = ) of 0.6 mm, inner radius 0.5 mm.
Isotropic plasma filled the drift channel entirely and its
density was 14
0 4.41 10pn = ⋅ cm-3. For analysis of trajec-
tories (1), we supposed that the initial energy of witness
bunch electrons is equal to the energy of drive bunch
electrons.
Fig. 2. Axial profile of the longitudinal force (blue
solid line) and axial profile of the transverse force
(red line) at the distance 0.45 mm from the wave-
guide axis. Drive bunch (the yellow rectangle) moves
from right to left. The cyan rectangle shows
the location of the electron witness bunch
In Fig. 2 are shown the axial profiles of longitudinal
and transverse forces that can act upon witness bunch
electrons. For the computation of the trajectories, the
initial location of the test electrons will be taken around
the third maximum of accelerating field 2.21z = mm
(see cyan rectangle in Fig. 2). One can see that this loca-
tion of test particles provides both acceleration and fo-
cusing simultaneously.
Fig. 3. Location of test witness bunch electrons in the
plane (x, z) accelerated by the wakefield of a drive
bunch. Initially the center of witness bunch is located
at a distance 2.21 mm behind the center of the drive
bunch. At the same radius are located 3 witness elec-
trons (at the head z=2.21-Lb/2, at the center z=2.21 an
at the tail z=2.21+Lb/2. Zero initial transverse velocity
of test electron was used in this computation
In Fig. 3 is presented the trajectories of test electrons
in the plane (y=0). At a travel distance of 8 cm a trans-
verse focusing deflection ~ 0.15 mm of the 0.45 mm
radius witness bunch is found. If we use a longer unit,
the minimal radius of the witness bunch can be reached
at z~14.8 cm where it is 0.07 mm. The aberration visible
in the “focal plane” z~14.8 cm is due to the deflection
of the focusing force from its linear dependence.
In Fig. 3, the trajectories of witness bunch electrons
are computed when the initial transverse velocity is ze-
ro. Similar trajectories of test particles for different
transverse initial velocities are shown in Fig. 4.
ISSN 1562-6016. ВАНТ. 2015. №6(100) 44
Fig. 4. The same as Fig. 3 except for different
ratios of initial radial to axial velocities:
r z= v / v /r zu uθ = : a) 0.001θ = ; b) 20.00θ = ;
c) 20.00 5θ =
We find that the initial transverse velocity does not
cause a considerable shift of “focal plane”. The width of
the witness bunch changes modestly there too. Further-
more, if the initial transverse velocity is greater than a
certain value (for our parameters this is 0.0025), some
of the test particle will deposit on the dielectric surface
(see Fig. 4,c).
Fig. 5. Radius of test electrons accelerated in the
wakefield of drive bunch. Initial velocities of test elec-
trons are max/ /r z bu u r rθ θ= = ⋅ , 3
max 2 10θ −= ⋅ .
The remaining parameters are the same as in Fig. 3
A more realistic situation of the transport of a wit-
ness bunch having initial energy spread when the initial
velocity of a test particle depends on its distance from
the axis is shown in Fig. 5. Minimal width of the wit-
ness bunch at the “focal plane” is ~0.06 mm, i.e. it is
about the same for all previously considered cases.
From this, one can see that the focusing of the wit-
ness bunch by the transverse field is strong and we can’t
avoid the over-compression of the accelerated bunch.
The only way remaining is to shorten the length of the
PDWA section so that the “focal plane” is located in a
vacuum portion of the waveguide.
One possibility to choose the lengths of the PDWA
cells and vacuum gap is: let the first PDWA cell be
7.5 cm, the length of the second PDWA cell be 6.5 cm,
and the vacuum gap length be 11 cm. For this case,
Fig. 6 shows the characteristics of the test particles dur-
ing the transport through the PDWA. In this example
the test electrons entering into the first PDWA cell do
not have a radial velocity.
Fig. 6. Transverse coordinate (a), energy gain (b),
shift from initial axial position (c) of test witness
bunch electrons accelerated by the wakefield of a
drive bunch travelling through two PDWA cells sep-
arated by a vacuum space. Initially the test electrons
are located at a distance 2.21 mm behind the center
of the drive bunch. Composite plot (d) shows energy
gain of test electrons in the plane z-32.7 cm versus
their axial shift from initial location. Yellow rectan-
gles mark the axial location of the PDWA cells
ISSN 1562-6016. ВАНТ. 2015. №6(100) 45
One can see that after passing the second PDWA cell
the motion of the test witness bunch particles is nearly
laminar. Their energy spread at the output of the second
PDWA cell is ±0.7 MeV (~2%) and the maximal dis-
placement of test particles from the resonance wave
phase is 2 microns. We note that the least displacement
and the largest energy gain has occurred for the on-axis
particles.
Fig. 7. The same in Figs. 6,a,b
for the plasma density increased by 5%, 01.05p pn n=
In Figs. 7 and 8 is demonstrated a change of charac-
teristics of the witness bunch upon varying the plasma
density from that used in the previous figures. One can
see that a 5% variation of the plasma density is not
harmful for the stable transport of the witness bunch
through the accelerator unit. When increasing the plas-
ma density there is a small divergence of the witness
bunch at the output of the second PDWA cell. Very
likely, it is connected with the change of the wavelength
of the total wakefield so that the test particles are dis-
placed from the optimal location (maximum of acceler-
ated and focusing field). More accurate placing of the
witness bunch could decrease the observed divergence.
CONCLUSIONS
One can avoid over-compression of the bunch radius
of an accelerated bunch inside the plasma cell by using
an array of plasma cells separated by vacuum spaces.
At the output of the second cell it is possible to ob-
tain laminar straight-line flow of the witness bunch.
A small variation of plasma density (tolerance) is
not significant for the proposed scheme of transporting
the accelerated bunch.
Fig. 8. The same in Figs. 6,a,b for the plasma density
reduced by 5%, 00.95p pn n=
ACKNOWLEDGMENTS
Work supported in part by NAS of the Ukraine pro-
gram "Perspective investigations on plasma physics,
controlled thermonuclear fusion and plasma technolo-
gies", Project P-1/63-2015 "Development of physical
principles of plasma-dielectric wakefield accelerator".
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4. Eric Esarey, Phillip Sprangle, Jonathan Krall, and
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5. K.L. Bane, P. Chen, and P.B. Wilson. On collinear
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Article received 05.10.2015
ТРАНСПОРТИРОВКА СГУСТКОВ В ДИЭЛЕКТРИЧЕСКОМ КИЛЬВАТЕРНОМ УСКОРИТЕЛЕ
С ПОМОЩЬЮ МАССИВА ПЛАЗМЕННЫХ ЯЧЕЕК
Р.Р. Князев, Т.К. Маршал, Г.В. Сотников
Предлагается использовать массив относительно коротких секций плазменно-диэлектрических кильва-
терных ускорительных (ПДКУ) модулей, разделенных вакуумными промежутками (без плазмы, хотя они
могут содержать диэлектрическую структуру), с цель избежать нежелательной перефокусировки ускоряемо-
го сгустка. Проведен расчет динамики ускоряемых частиц в такой решетке ускорительно-дрейфовых секций
ПДКУ. Для расчета использованы параметры сгустков, имеющиеся в SLAC. Диэлектрическая структура на
основе плавленого кварца обеспечивает рабочую частоту ~ 350 ГГц. Найдены длины плазменной и вакуум-
ной секций, обеспечивающих устойчивую транспортировку ускоряемого сгустка. Определены размеры сгу-
стка в фокальной плоскости.
ТРАНСПОРТУВАННЯ ЗГУСТКІВ У ДІЕЛЕКТРИЧНОМУ КІЛЬВАТЕРНОМУ ПРИСКОРЮВАЧІ
ЗА ДОПОМОГОЮ МАСИВУ ПЛАЗМОВИХ СЕКЦІЙ
Р.Р. Князєв, Т.К. Маршал, Г.В. Сотніков
Пропонується використовувати масив відносно коротких секцій плазмово-діелектричних кільватерних
прискорювальних (ПДКП) модулів, розділених вакуумними проміжками (без плазми, хоча вони можуть міс-
тити діелектричну структуру), з метою уникнути небажаного перефокусування згустку, що прискорюється.
Проведено розрахунок динаміки частинок, що прискорюються, у такій решітці прискорювально-дрейфових
секцій ПДКП. Для розрахунків використані параметри згустків, наявні в SLAC. Діелектрична структура на
основі плавленого кварцу забезпечує робочу частоту ~ 350 ГГц. Знайдено довжини плазмової й вакуумної
секцій, які забезпечують стійке транспортування згустку, що прискорюється. Визначені розміри згустку у
фокальній площині.
|