Ion separation in a plasma mass filter based on the band gap filter principle
The mass separation in a multicomponent collisionless plasma rotating in an axial homogeneous magnetic field and a radial electric field with dc and ac components at the parametric resonance conditions is considered. For given conditions, it is shown that when the variable component of a radial elec...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1947032023-11-29T10:59:07Z Ion separation in a plasma mass filter based on the band gap filter principle Ilichova, V.O. Low temperature plasma and plasma technologies The mass separation in a multicomponent collisionless plasma rotating in an axial homogeneous magnetic field and a radial electric field with dc and ac components at the parametric resonance conditions is considered. For given conditions, it is shown that when the variable component of a radial electric field with ω=0,57 Ω is superposed on the dc component, the resonant uranium dioxide ions are ejected into the wall of the plasma mass filter, which is currently being developed for the separation of nuclear fuel and fission products. The correlation between the oscil-lation frequency of ac voltage component with the modified (vortex) ion-cyclotron frequency is shown. Розглянуто розподіл іонів за масами в багатокомпонентній беззіткненій плазмі, що обертається в осьовому однорідному магнітному полі та радіальному електричному полі з компонентами постійного та змінного струму в умовах параметричного резонансу. Для заданих умов показано, що при суперпозиції змінної компоненти радіального електричного поля з частотою коливань ω = 0,57 Ω та постійної компоненти, резонансні іони двоокису урану виходять на бічну стiнку плазмового фільтра мас, який в даний час розробляється для розділення ядерного палива та продуктів поділу. Показана кореляція частоти коливань з модифікованою іонно-циклотронною частотою. Рассмотрено разделение ионов по массам в многокомпонентной бесстолкновительной плазме, вращающейся в осевом однородном магнитном поле и радиальном электрическом поле с постоянной и переменной компонентами в условиях параметрического резонанса. Для заданных условий показано, что при суперпозиции переменной компоненты радиального электрического поля с частотой колебаний ω =0,57 Ω и постоянной компоненты, резонансные ионы диоксида урана выходят на боковую стенку плазменного фильтра масс, который в настоящее время разрабатывается для разделения ядерного топлива и продуктов деления. Показана корреляция частоты колебаний с модифицированной ионно-циклотронной частотой. 2019 Article Ion separation in a plasma mass filter based on the band gap filter principle / V.O. Ilichova // Problems of atomic science and technology. — 2019. — № 1. — С. 138-141. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 28.41Kw http://dspace.nbuv.gov.ua/handle/123456789/194703 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies |
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Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies Ilichova, V.O. Ion separation in a plasma mass filter based on the band gap filter principle Вопросы атомной науки и техники |
| description |
The mass separation in a multicomponent collisionless plasma rotating in an axial homogeneous magnetic field and a radial electric field with dc and ac components at the parametric resonance conditions is considered. For given conditions, it is shown that when the variable component of a radial electric field with ω=0,57 Ω is superposed on the dc component, the resonant uranium dioxide ions are ejected into the wall of the plasma mass filter, which is currently being developed for the separation of nuclear fuel and fission products. The correlation between the oscil-lation frequency of ac voltage component with the modified (vortex) ion-cyclotron frequency is shown. |
| format |
Article |
| author |
Ilichova, V.O. |
| author_facet |
Ilichova, V.O. |
| author_sort |
Ilichova, V.O. |
| title |
Ion separation in a plasma mass filter based on the band gap filter principle |
| title_short |
Ion separation in a plasma mass filter based on the band gap filter principle |
| title_full |
Ion separation in a plasma mass filter based on the band gap filter principle |
| title_fullStr |
Ion separation in a plasma mass filter based on the band gap filter principle |
| title_full_unstemmed |
Ion separation in a plasma mass filter based on the band gap filter principle |
| title_sort |
ion separation in a plasma mass filter based on the band gap filter principle |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2019 |
| topic_facet |
Low temperature plasma and plasma technologies |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/194703 |
| citation_txt |
Ion separation in a plasma mass filter based on the band gap filter principle / V.O. Ilichova // Problems of atomic science and technology. — 2019. — № 1. — С. 138-141. — Бібліогр.: 10 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT ilichovavo ionseparationinaplasmamassfilterbasedonthebandgapfilterprinciple |
| first_indexed |
2025-07-16T22:10:06Z |
| last_indexed |
2025-07-16T22:10:06Z |
| _version_ |
1837843151486713856 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2019. №1(119)
138 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2019, № 1. Series: Plasma Physics (25), p. 138-141.
ION SEPARATION IN A PLASMA MASS FILTER BASED ON THE BAND
GAP FILTER PRINCIPLE
V.O. Ilichova
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: ilichovav@gmail.com
The mass separation in a multicomponent collisionless plasma rotating in an axial homogeneous magnetic field
and a radial electric field with dc and ac components at the parametric resonance conditions is considered. For given
conditions, it is shown that when the variable component of a radial electric field with 57.0 is superposed on
the dc component, the resonant uranium dioxide ions are ejected into the wall of the plasma mass filter, which is
currently being developed for the separation of nuclear fuel and fission products. The correlation between the oscil-
lation frequency of ac voltage component with the modified (vortex) ion-cyclotron frequency is shown.
PACS: 28.41Kw
Plasma methods for SNF (spent nuclear fuel) repro-
cessing are a promising alternative to radiochemical
technologies. However, there is a number of problems
with plasma separation of fission products (FPs) and
nuclear fuel (NF). The difficulties are connected with
SNF multicomponent composition, the proximity of
masses in case of isotopes and the presence of the mul-
ticharged ions. Thus, many problems appear and many
variants of their solution are considered [1, 2]. In the
light of this so-called ion band gap filter is of interest,
which provides various modes of ion separation in a
plasma by mass [3].
This paper considers the plasma mass filter for sepa-
rating NF and FPs [4] based on the band gap filter prin-
ciple. Below the conditions for the separation of ions by
mass (mass/charge) in a multicomponent collisionless
plasma rotating in an axial homogeneous magnetic field,
zB , and a radial electric field,
rE , with dc and ac com-
ponents are studied. The radial electric field
rE is gen-
erated by coaxial electrodes – 6. The oscillation fre-
quency, , for the ac component of
rE is set by a tuner
– 7.
Fig. 1. Schematic view of the plasma mass filter:
1 – 4 – of the longitudinal collector; 5 – end collector;
6 – coaxial system of electrodes; 7 – tuner;
8 – system of solenoids
If
rE periodically changes in time, its value can be
represented as a superposition of the ac and dc compo-
nents. In frequency terms this corresponds to [3]:
)cos( tEacEdcE , (1)
where ωE – angular frequency which includes; ωEdc –
constant and ωEac – variable components.
At a sinusoidal change of ωE, the Mathieu equation
for parametric resonance to determine the frequency of
orbit oscillations in a plasma can be used:
0)]2cos(4[
4
1 2
s
d
sd
. (2)
The solution of the Mathieu equation is connected with
determination of the coefficients α and .
2/t ,
2
2
/)
4
(
Edc
,
24
Eac .(3)
Frequency intervals in which the ions have localized
and non-localized orbits are shown in Fig. 2.
Fig. 2. A graph of the first few confined and unconfined
regions of the solution for s in - space:
4α0>-32β2 for the interval (0); 1–8β<4α1<1+8β for
the interval (1); 4–16/3β2<4α2(β)<4+80/3β2 for the
interval (2). The dashed regions are the unconfined
regions [3]
The combinations of the coefficients and ,
which correspond to dc and ac components of the radial
electric field
rE , determine the penetration to the zones
of magnetized / unmagnetized ions. To determine the
conditions for the separation of ions in the plasma mass
filter [4], let's consider the frequency characteristics at
ISSN 1562-6016. ВАНТ. 2019. №1(119) 139
the boundaries of the instability intervals, that is, at the
threshold of the transition from a stable state, where the
ions are magnetized, to the unstable one, where the ions
are not magnetized. This correlates with the equation of
the forces balance in the plasma mass filter with posi-
tive radial electric field, that is discussed below.
There are three forces acting on a charged particle
(ion) in a collisionless plasma rotating in EH fields
[5]: centrifugal – 2
iic rmF , electric –
rE eEF ,
and magnetic –
ziB BerF , where mi – mass of i-kind
ion, i is the angular rotation frequency for i-kind ion, r
is the particle's distance to the axis of rotation,
rE is
radial electric field strength proportional to r
( rEr / =const),
zB is a value of magnetic field on the
axis, and e – the charge of the electron. Rotation of a
plasma is obtained by its interaction with radial electric
field,
rE and axial magnetic field,
zB .
In the plasma mass filters with a positive potential,
the electric and centrifugal forces are directed outward,
and Lorenz force is directed inward. An equilibrium
conditions in a radial direction can be expressed:
0 rF , (4)
or
02 zirii BereErm . (5)
The ion cyclotron freduency for the i-kind ion is
written:
iz mzeB / . (6)
Thus, the solution of equation becomes:
))/(411(2/ zri rBE , (7)
where
i is an angular freguency of the i-kind ion.
The critical options of plasma rotation can be deter-
mined from the discriminant of the equation equal to
zero, that is, at 1)/(4 zr rBE , which corresponds to
RrBBEE cr
zz
cr
rr ,, . In turn, from the solution of
the Mathieu equation this state corresponds to the point
( 0,0 ) (Fig. 2) at the boundary of the instability
interval (0) [3]:
25
0 24 . (8)
At 0 , separation of ions into heavy and light ions
occurs in the mode of operation of the Ohkawa (Archi-
medes) plasma mass filter [5]. Separation mass of
crM
is determined by critical value of electric field cr
rE r and
magnetic field cr
zB :
)4/()( 2 cr
r
cr
zcr EBzeRM , (9)
or
)8/()( 22
dc
cr
zcr UBzeRM , (10)
where 0dcU is the positive potential of electric field
along the longitudinal axis, R is the radius of the cylin-
drical chamber.
In this case, the light ions with
cri Mzm / have lo-
calized orbits, and the heavy ions
cri Mzm / have
non-localized orbits. The parameters RBE cr
z
cr
r ,, deter-
mine the conditions of separation process in the plasma
mass filter. For 1)/(4 zr rBE , that is, for
cr
rr EE 0 , equation (5) has a real solution (7), and
ions with mass
cri Mzm / have localized orbits.
To set the parameters for ion separation in a multi-
component collisionless plasma rotating in EH fields,
it is necessary to consider the modified (vortex) cyclo-
tron frequency
i , that determines the phase of decel-
eration and acceleration for i-kind singly charged ion
[6]:
cr
i
i
M
m
1 . (11)
At 0 i
the value of
i is equal to the sub-
harmonic of the cyclotron frequency ( 2/i ) [6]. In
this case, a system with rotating plasma appears on the
boundary of the instability interval (0) at the point
0,0 (see Fig. 2).
At 1)/(4 zr rBE , expression (7) has imaginary
roots. In this case, the ions with
cri Mzm / have non-
localized orbits in the instability interval (0), and the
forces in (5) are not balanced (see Fig. 2).
The instabilities in a plasma are associated with the
presence of oscillations. In particular, a harmonic analy-
sis of plasma oscillations in a rotating plasma at cyclo-
tron resonance instability conditions showed that there
was a number of harmonics of the fundamental ion cy-
clotron frequency in the spectrum [7]. In addition, the
instability in a plasma due to the relative motion of
plasma components and nonlinear effects in the move-
ment of charged particles in the electric field under os-
cillations can lead to the appearence of a parametric
resonance, that may influence on an ion separation pro-
cess [8, 9].
The growth of the ac component of a radial electric
field (at growth ) for the critical parameters of plasma
rotation in the plasma mass filter (at 0 , see Fig. 2)
leads to the transition to the instability interval (1) cor-
responding to the main parametric resonance.
The resonant conditions for the instability interval
(1) in the frequency terms are given by [3]:
2
22 8
mR
zeU dc , (12)
where is the frequency of ac voltage component.
If 0dcU the oscillation frequency in the gap of
frequency interval (1) is equal to the ion cyclotron fre-
quency, . In this case, the acceleration of the
resonant ions occurs at the fundamental harmonic .
These conditions determine the separation regime for
isotope separation, similar to the ICR (ion cyclotron
resonance) method [3].
In the case of 0dcU , under the conditions of par-
ametric resonance, another separation mode can be real-
ized, when in a plasma mass filter, together with ions of
cri Mzm / , it is possible to allocate the target ions of
cri Mzm / [3].
140 ISSN 1562-6016. ВАНТ. 2019. №1(119)
This separation mode is considered for ejection of
uranium dioxide ions to the longitudinal collector of the
plasma mass filter (Fig. 1).
Let's determine the radius R for the separation of
the molecular ions of the multicomponent oxides with
cri Mzm / at initial conditions T 0.1=Bz
,
0E =400 V/m and 400crM . In accordance with ex-
pression (9) m 1.3=R .
The oscillation frequency for the resonant condi-
tions (12) in mass terms [3] becomes:
cr
i
zM
m
1 . (13)
Thus, at paramatric resonance conditions the fre-
quency is equal to the modified ion cyclotron fre-
quency
i (11). So, there is correlation between equa-
tions (2) and (5) in respect to
i , that is, at parametric
resonance conditions, the oscillation frequency of
the resonant (i-kind) ion orbit is connected with the self-
oscillations of i-kind ion determined at critical plasma
rotation options.
Thus, for 400crM and 270/ zmi
, which corre-
sponds to to the molecular ions UO2
+, from (13) we ob-
tain ω = 0.57 Ω. It follows, that at superposition of ac
voltage component with ω = 0.57 Ω and dc component
the uranium dioxide ions are filtered out to the collector
of the plasma mass filter (see Fig. 1). This is confirmed
in the calculation of the trajectories for the resonant
uranium dioxide ions at their ejection into the chamber
wall of R = 1.3 m (Fig. 3,a).
a
b
Fig. 3. Trajectories of ions in the plasma mass filter [4]
at oscillation frequency ω = 0.57 Ω (UO2
+) of ac volt-
age component: UO2
+ (a); La2O3
+ for initial conditions
described in [10] (b)
From expression (6) the value of Ω for BZ=0.1 T and
270/ zmi
is defined: Ω(UO2
+) = 3.56104 rad/s, and,
correspondingly, f = 5.6 kHz (f=Ω/2π).
The width of the parametric resonance is determined
according [3]:
22
)2(4
m
m
, (14)
where ( 2 ) – is the growth of the amplitude of oscil-
lations.
The transition to the interval of instability (1) at
cr
rr EE is carried out at the boundary
)8/1,0( (see Fig. 2).
The value of was obtained from the boundary
equation:
81)(4 1
(15)
Substituting the value of in (14), mm may be
written as:
22
2
m
m
. (16)
At ω=0.57 Ω the resonance width becomes
25,0
m
m
.
Thus, in the resonant conditions, the ions with mass
numbers of 270±68, that is, the total spectrum of single-
charged actinide ions and their oxides can reach to the
longitudinal collector.
As can be seen (Fig. 3,b), in these conditions, the
mass corresponding to single-charged molecular ions of
lanthanide oxides are also filtered out to m 1.3=R . In
order to exclude these ions from the resonant condi-
tions, the operating frequency for the tuner should be
ω < 0.57 Ω (UO2
+). The results of calculations [10]
showed that this problem can be solved at exact value of
ω = 0.5 Ω (UO2
+), that is, a.c. voltage component must
be tuned to a radio frequency of 2.8 kHz at given initial
conditions.
CONCLUSIONS
1. The correlation between the ion orbit oscillation
frequency and the modified (vortex) ion-cyclotron fre-
quency in parametric cyclotron mass filter is shown.
2. For given conditions, it is shown that when ac
voltage component with oscillation frequency
ω = 0.57 Ω (UO2
+) is superposed on the dc component,
the resonant uranium dioxide ions are ejected into the
wall of the plasma mass filter [4].
3. For given conditions, the resonance width has
been determined: mm =270±68. Thus, to the longi-
tudinal collector, in addition to the uranium dioxide ions
it is possible to filter out the ions of actinides and their
oxides.
4. An analysis of the results showed that for the sep-
aration of the molecular ions of actinides and lantha-
nides oxides in the mass filter under consideration,
a.c.voltage component must be tuned to
ω = 0.5 Ω (UO2
+)
.
ISSN 1562-6016. ВАНТ. 2019. №1(119) 141
ACKNOWLEDGEMENTS
The author expresses the gratitude to
Prof. V. Yuferov for fruitful discussions.
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Article received 12.12.2018
СЕПАРАЦИЯ ИОНОВ В ПЛАЗМЕННОМ ФИЛЬTРЕ МАСС С ПРИНЦИПОМ ДЕЙСТВИЯ
ПОЛОСОВОГО ФИЛЬТРА
В.О. Ильичева
Рассмотрено разделение ионов по массам в многокомпонентной бесстолкновительной плазме,
вращающейся в осевом однородном магнитном поле и радиальном электрическом поле с постоянной и
переменной компонентами в условиях параметрического резонанса. Для заданных условий показано, что
при суперпозиции переменной компоненты радиального электрического поля с частотой колебаний
ω=0,57 Ω и постоянной компоненты, резонансные ионы диоксида урана выходят на боковую стенку плаз-
менного фильтра масс, который в настоящее время разрабатывается для разделения ядерного топлива и
продуктов деления. Показана корреляция частоты колебаний с модифицированной ионно-циклотронной
частотой.
СЕПАРАЦІЯ ІОНІВ У ПЛАЗМОВОМУ ФІЛЬТРІ МАС З ПРИНЦИПОМ ДІІ ПОЛОСОВОГО
ФІЛЬТРА
В.О. Ільічова
Розглянуто розподіл іонів за масами в багатокомпонентній беззіткненій плазмі, що обертається в осьово-
му однорідному магнітному полі та радіальному електричному полі з компонентами постійного та змінного
струму в умовах параметричного резонансу. Для заданих умов показано, що при суперпозиції змінної
компоненти радіального електричного поля з частотою коливань ω = 0,57 Ω та постійної компоненти, резо-
нансні іони двоокису урану виходять на бічну стiнку плазмового фільтра мас, який в даний час
розробляється для розділення ядерного палива та продуктів поділу. Показана кореляція частоти коливань з
модифікованою іонно-циклотронною частотою.
|