The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M
The modelling of the radial emissivity profiles of Hα and Hβ lines radiated from hydrogen plasma of the torsatron Uragan-3M in a typical operational regime requires the usage of the programming code KN1D to consider a balance of atom and molecule fluxes on the walls. For this purpose, the reflection...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2017
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irk-123456789-1221142017-06-28T03:02:42Z The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M Bondarenko, V.N. Petrushenya, A.A. Магнитное удержание The modelling of the radial emissivity profiles of Hα and Hβ lines radiated from hydrogen plasma of the torsatron Uragan-3M in a typical operational regime requires the usage of the programming code KN1D to consider a balance of atom and molecule fluxes on the walls. For this purpose, the reflection and re-emission coefficients were calculated of H atoms and H₂ molecules leaving the plasma and impinging on the plasma-facing surfaces of the stainless steel casings of a helical winding. Моделирование радиальных профилей интенсивности линий Hα и Hβ, излучённых из водородной плазмы торсатрона Ураган-3М в типичном рабочем режиме, требует использования программного кода KN1D для рассмотрения баланса атомных и молекулярных потоков на стенках. С этой целью были вычислены коэффициенты отражения и реэмисии атомов H и молекул H₂, покидающих плазму и падающих на обращённые к плазме поверхности кожухов винтовой обмотки из нержавеющей стали. Моделювання радіальних профілів інтенсивності ліній Hα і Hβ, випромінених з водневої плазми торсатрона Ураган-3М у типовому робочому режимі, вимагає використання програмного коду KN1D для розгляду балансу атомних і молекулярних потоків на стінках. З цією метою були обчислені коефіцієнти відбиття і реемісії атомів H і молекул H₂, які покидають плазму і падають на повернені до плазми поверхні кожухів гвинтової обмотки з нержавіючої сталі. 2017 Article The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M / V.N. Bondarenko, A.A. Petrushenya // Вопросы атомной науки и техники. — 2017. — № 1. — С. 14-17. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.25.Ya, 52.55.Hc, 52.25.-b, 52.25.Tx http://dspace.nbuv.gov.ua/handle/123456789/122114 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Магнитное удержание Магнитное удержание |
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Магнитное удержание Магнитное удержание Bondarenko, V.N. Petrushenya, A.A. The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M Вопросы атомной науки и техники |
| description |
The modelling of the radial emissivity profiles of Hα and Hβ lines radiated from hydrogen plasma of the torsatron Uragan-3M in a typical operational regime requires the usage of the programming code KN1D to consider a balance of atom and molecule fluxes on the walls. For this purpose, the reflection and re-emission coefficients were calculated of H atoms and H₂ molecules leaving the plasma and impinging on the plasma-facing surfaces of the stainless steel casings of a helical winding. |
| format |
Article |
| author |
Bondarenko, V.N. Petrushenya, A.A. |
| author_facet |
Bondarenko, V.N. Petrushenya, A.A. |
| author_sort |
Bondarenko, V.N. |
| title |
The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M |
| title_short |
The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M |
| title_full |
The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M |
| title_fullStr |
The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M |
| title_full_unstemmed |
The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M |
| title_sort |
reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron uragan-3m |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2017 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/122114 |
| citation_txt |
The reflection and re-emission coefficients of hydrogen particles impinging from plasma on the wall in the torsatron Uragan-3M / V.N. Bondarenko, A.A. Petrushenya // Вопросы атомной науки и техники. — 2017. — № 1. — С. 14-17. — Бібліогр.: 14 назв. — англ. |
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Вопросы атомной науки и техники |
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ISSN 1562-6016. ВАНТ. 2017. №1(107)
14 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 14-17.
THE REFLECTION AND RE-EMISSION COEFFICIENTS OF
HYDROGEN PARTICLES IMPINGING FROM PLASMA ON THE WALL
IN THE TORSATRON URAGAN-3M
V.N. Bondarenko, A.A. Petrushenya
Institute of Plasma Physics of the NSC KIPT, Kharkov, Ukraine
E-mail: vnbondarenko65@kipt.kharkov.ua
The modelling
of the radial emissivity profiles
of Hα and Hβ lines radiated from hydrogen plasma of the torsatron
Uragan-3M in a typical operational regime
requires the usage of the programming code
KN1D to consider a balance
of atom and molecule fluxes
on the walls. For this purpose, the reflection and re-emission coefficients
were
calculated of H atoms and H2 molecules
leaving the plasma and impinging on the plasma-facing surfaces
of the
stainless steel casings
of a helical winding.
PACS: 52.25.Ya, 52.55.Hc, 52.25.-b, 52.25.Tx
INTRODUCTION
The methods of optical spectroscopy of hydrogen
plasma created with RF discharge in the torsatron
Uragan-3M (l = 3, m = 9) are associated with computing
the emissivity profiles of Hα and Hβ spectral lines
radiated from plasma. Such profiles have been measured
in the experiments [1-3]. The numerical modeling of
torsatron plasma with the programming code KN1D [4]
provides a possibility to consider a hydrogen atom and
molecule flux balance on a stainless steel wall at the
given time moment of the RF discharge. The ions H
+
and H2
+
do not take part in the balance by reason of
peculiarities of the movement. The balance has to be
based on the reflection and re-emission coefficients of H
atoms and H2 molecules impinging from plasma on
plasma-facing surfaces. In this study these coefficients
are used at a normal incidence of particles.
An objective of this study is calculation of the
reflection and re-emission coefficients of hydrogen
atoms and molecules on the plasma-facing surface,
using the program SRIM [5] and the solution of a
diffusion equation. The coefficients were used as the
input data of the code KN1D [4] in order to compute the
particle flux to the plasma-facing surface and from it,
and the balance of the fluxes at a quasi-stationary stage
of RF discharge.
1. EXPERIMENTAL CONDITIONS
The plasma-facing surfaces are: 1) the casings of a
helical winding of a magnetic system, 2) the remote
walls outside of the helical winding of the torsatron. In
Fig. 1 the poloidal cross-section D-D of the magnetic
system is shown. Each casing is a shell on one of three
turns (l = 3) of the helical winding. The walls and
casings are made of stainless steel of the type
12KH18N10T (Fe, Cr, Ni, Mn, and others).
In this study, we consider a particle flux balance
only on the plasma-facing surfaces which are inside the
helical winding. The balance of fluxes on the remote
walls is out of the scope of this paper. To guide the eye
in Fig. 1, a poloidal circle was inscribed between the
casings 1, 2 and 3 in D-D, and the circle’s vertical
diameter AB (D = 0.38 m) was drawn between the
casings 2 and 3. The plasma-facing surface is on the
boundary of the casings and the poloidal circle if the
latter moves through all poloidal cross-sections.
Fig. 1. The poloidal cross-section D-D. R is a major
radius of the torsatron. The magnetic flux surfaces are
located between the casings 1, 2, and 3. The vertical
diameter AB of a poloidal circle connects
the casings 2 and 3
To calculate the reflection and re-emission
coefficients, we have studied the parameters of
hydrogen plasma of the typical RF discharge in the
torsatron Uragan-3M at a toroidal magnetic field
B = 0.72 T.
The RF pulse of a three-half-turn antenna with
anode voltage of U2 = 6 kV and duration of 20 ms
creates the preliminary ionization of the hydrogen.
Immediately after the shutdown of the RF pulse, the
next pulse of a frame-type antenna with anode voltage
of U1 = 7 kV and duration of 40 ms is switched on and
produces the plasma with a line-averaged density of
≤ 2 × 10
18
m
-3
and an electron temperature of
Te ≤ 0.5 keV. The time moment t0 = 55 ms of
measurements is
in the middle of the second RF pulse
ISSN 1562-6016. ВАНТ. 2017. №1(107) 15
creating and sustaining the plasma. Before both pulses,
a hydrogen pressure in a vacuum vessel was
PH2 = 1.1 × 10
-5
Torr, and a density of hydrogen
molecules was nini = 3.2 × 10
17
m
-3
.
2. THE REFLECTION AND RE-EMISSION
OF HYDROGEN PARTICLES
H
+
and H2
+
ions leaving plasma do not impinge on
the plasma-facing surfaces of the casings directly
because the ions move in a divertor region to the rear
and lateral sides of the casings. After backscattering or
re-emission from the surfaces, the ions contribute
negligibly to the atom or molecule flux returning from
remote walls to the plasma. The flux Гi = 2 × 10
20
m
-2
s
-1
of H
+
ions drifting from the plasma was estimated at the
plasma edge with the code KN1D, taking an average
minor radius of the plasma = 0.125 m. The flux Γi is
close to the flux Г = 3 × 10
20
m
-2
s
-1
measured by
Langmuir probes in the divertor region in the similar
experimental conditions [6].
Therefore, here we take into account only the atom
and molecule fluxes leaving plasma and impinging on
the plasma-facing surfaces where neutrals are involved
in the processes of two types: reflection and re-
emission.
2.1. THE REFLECTION OF ATOMS
The reflection process of impinging H atoms is, in
principle, backscattering of them from atoms of the
surface or atoms in the bulk of metal. A process product
is H atoms [5]. We identify two types of atoms
impinging from plasma on the plasma-facing surfaces,
according to atom kinetic energy E0. Therefore, two
processes of reflection from the surface were taken into
account:
H + wall → H, (1)
HCX + wall → H. (2)
This means that the atoms impinge on the plasma-
facing surface and reflect from it. The first type is the
low-energy atoms (E0 = 3…10 eV), the second type –
the high-energy charge exchange (CX) atoms
( 0 ≈ 120 eV). An energy range in process (1) was
found using the code KN1D. The value 0 in process
(2) is some average energy of the CX atom flux, also
estimated with this code.
For the conditions of these experiments (Section 2),
the energy of CX atoms is, approximately, in the range
120 eV…4 keV as is shown in Subsection 3.4.
The reflection coefficient of the atom flux is
RN = I/I0. It was evaluated with a program SRIM [5] as a
function of kinetic energy E0, where I0 is impinging
flux, I – reflected flux. The energy reflection coefficient
was determined using a formula shown in [7].
2.2. THE RE-EMISSION IN THE CASE
OF IMPINGING ATOMS
The process of molecular re-emission is associated
with implantation of impinging atoms into the bulk of
metal [8-10]. In this case, an implanted H atom can
diffuse to the surface and recombine with other atom to
a molecule (H + H → H2) which can leave the surface
due to desorption. The left-hand sides of processes (3)
and (4) coincide with those in (1) and (2), respectively,
but the process product is a molecule:
H + wall → H2, (3)
HCX + wall → H2. (4)
The re-emission coefficient j0 = J0/I0i of the desorbed
flux was determined using formulas (5) and (6). Here J0
is desorption flux of molecules, I0i = I0(1 - RN) – flux
incoming into the bulk of metal, RN – the reflected part
of atoms [9, 10].
The hydrogen concentration u(x,t) at the depth x, at
the time moment t is included in diffusion equation (5)
with an ion source located in the bulk. The boundary
condition (6) implies the balance between the diffusion
flux from the source to the surface and the desorption
flux from the surface [9]:
∂u(x,t)/∂t = D∂
2
u(x,t)/∂x
2
+ I0iφ(x), 0 < x < ∞, (5)
D∂u(x,t)/∂x = Ku
2
(x,t), x = 0. (6)
Here D is the diffusion coefficient, K – the
recombination coefficient at the surface (x = 0), I0iφ(x) –
the ion source. The source φ(x) = δ(x - Rp) in (5) is
located at the depth of an ion projected range Rp in
metal. The solution of this system is expressed with the
integral equation given in [9].
2.3. THE REFLECTION AND RE-EMISSION OF
MOLECULES
A temperature of low-energy molecules escaping
from the plasma-facing surface corresponds to the
temperature of the surface [4], which is equal to ~35°C
in the experiments.
To know more about the processes on the stainless
steel surface of the casing, we show here some results of
a quantum mechanical study of the dynamics of H2
molecule dissociation on the Ni (100) surface [11]. The
activation barrier VA to molecular adsorption, the barrier
VD to dissociation (H2 → H + H), and the barrier VH to
H atom diffusion along the metal surface are related to
these processes.
There are three examples with the different ratios of
the barrier heights VD and VH [11]:
1) VD < VH, the reflection process only; H2 molecules
dissociate to H atoms which reflect (R = 99 %) from the
barrier VH and desorb immediately to a gas phase;
2) VD VH, re-emission dominates; H2 molecules
dissociate to H atoms; the atoms travel along the surface
and can recombine to molecules which can desorb;
3) VD VH, reflection and re-emission are possible.
The process product is a molecule:
H2 + wall → H2. (7)
As is shown in [11], the reflection and re-emission
coefficients of H2 molecules are low at low kinetic
energy of molecules, corresponding to the casing
temperature of ~35°C. For the plasma-facing surface of
stainless steel casings we assumed that the sum of both
these coefficients, j0m7, is equal to the experimental
coefficient 0.07 given for H2 molecules [12].
16 ISSN 1562-6016. ВАНТ. 2017. №1(107)
The average kinetic energy of molecules passed
through the plasma is slightly less before the plasma-
facing surface than that of molecules escaping from this
surface as was calculated with the code KN1D. In this
case, we decreased the coefficient j0m7 to the value of
0.05, following to the explanations related to
Fig. 9 in [11].
2.4. THE COEFFICIENTS RN AND j0 FOR ATOMS
In Fig. 2, the reflection coefficient RN of H atoms,
impinging on the plasma-facing surface of the stainless
steel casing in processes (1) and (2) is presented as a
function of atom kinetic energy E0. Also, the re-
emission coefficient j0 for processes (3) and (4), and the
total coefficient RN + j0 are plotted in this figure.
Fig. 2. a) The reflection coefficient RN; b) the re-
emission coefficient j0; c) the total coefficient RN + j0
are the functions of kinetic energy E0 of H atoms
impinging on the stainless steel surface
To determine approximately the energies of CX
atoms, we considered the results of [2, 13], related to
the low-density plasma discharges in Uragan-3M, with
the experimental conditions similar to those shown in
Section 2.
The ion energy distributions in the range
0.4…4 keV, and the corresponding ion temperatures in
the range 0.4…0.55 keV, presented in [13], were
obtained with CX neutral particle diagnostics. These
results and the results of Doppler spectrometry,
described in [2], indicate the temperatures of ~40 and
~300 eV of C
4+
ions, and the comparable temperatures
of H
+
ions. Here we calculated the H
+
ion energy
distributions and estimated the average energy
0 ≈ 120 eV of CX atoms in energy distributions, using
formula (2A11) from [14], as well as formulas and the
data of Fig. 8 from [13].
The energy of CX atoms is, approximately, in the
range 120 eV…4 keV. The energy range in Fig. 2
covers the ranges of low-energy H atoms and high-
energy CX atoms.
3. THE BALANCE OF FLUXES
The impinging flux of atoms in processes (1)-(4) can
be divided into the parts of reflected atoms, desorbed
molecules, and implanted atoms, according to [9, 10]. In
process (7) the impinging flux of molecules is modified
into the fluxes of reflected and desorbed molecules as
was shown for H2 dissociation on Ni (100) [11].
Since the condition of the balance of atom and
molecule fluxes has to be achieved, the net mass flux
from the wall is zero (100 % recycling) [4]. According
to this, the net flux of molecules from the wall (a
difference of desorption flux and impinging flux) must
be equal to the impinging flux of atoms. It is necessary
to decrease the latter by the flux of reflected and
desorbed atoms on condition that they exist.
The balance condition was applied at the quasi-
stationary stage of the RF discharge, in the middle of
the RF pulse of the frame-type antenna, creating and
sustaining the plasma. The diagnostic oscillograms
corresponding to the plasma density, the electron
temperature, and the brightness of the Hα and Hβ
spectral lines were changed very slowly at the moment
t0. The fluxes were modeled with the code KN1D along
the diameter AB (see Fig. 1).
The sum of the terms I01RN1 and I02RN2
corresponding to the left-hand sides in (1) and (2) is
equal to the sum of the reflected flux terms I1 and I2
of
the right-hand sides. The impinging flux terms are I01 =
4.0 × 10
20
m
-2
s
-1
and I02 = 7.4 × 10
20
m
-2
s
-1
. The
reflection coefficients are RN1 and RN2. The sum of the
reflected flux terms is 1.2 × 10
20
+ 2.4 × 10
20
=
3.6 × 10
20
m
-2
s
-1
. The values of the reflection and re-
emission coefficients are shown above.
The sum of other terms I03j03(1 - RN1), I04j04(1 - RN2),
and I07j0m7 in the left-hand sides of (3), (4) and (7) is
equal to the sum of the desorption flux terms I3, I4 and I7
in the right-hand sides. The impinging flux terms of
atoms in (3), (4), and molecules in (7) are I03 = I01, I04 =
I02, and I07 = 2.5 × 10
18
m
-2
s
-1
. For impinging atoms, the
re-emission coefficients are j03 and j04. The total
reflection and re-emission coefficient of molecules is
j0m7. The sum of the flux terms is 9.5 × 10
18
+ 2.3 × 10
19
+ 1.3 × 10
17
= 3.3 × 10
19
m
-2
s
-1
.
In the space between the plasma and the plasma-
facing surfaces, the molecular flux exists with Г0,sp =
1.5 × 10
20
m
-2
s
-1
, not crossing the plasma and impinging
on these surfaces. The flux is
reflected and desorbed
from the surfaces with Гsp = 1.1 × 10
19
m
-2
s
-1
, and the
coefficient j0m7 = 0.07.
In the middle of the second RF pulse, the molecular
density n0 on the plasma-facing surfaces, calculated
with the code KN1D, is lower by ~35 % than the
density nini before the pulses.
CONCLUSIONS
In this paper, the reflection and re-emission
coefficients are presented for the fluxes of H atoms and
H2 molecules impinging with given kinetic energy from
hydrogen plasma on the plasma-facing surface of the
stainless steel casings on a helical winding during a
typical RF discharge in the torsatron Uragan-3M.
The fluxes of H
+
and H2
+
ions do not take part in
reflection and re-emission on the plasma-facing surface
since the ions move mainly to the rear and lateral sides
of the casings.
ISSN 1562-6016. ВАНТ. 2017. №1(107) 17
The reflection and re-emission coefficients of H
atoms and H2 molecules are used in the code KN1D.
The values of the fluxes impinging on the plasma-facing
surfaces and the values of the reflection and desorption
fluxes were calculated. An atom and molecule flux
balance was considered at the quasi-stationary stage of
the RF discharge creating and sustaining the plasma in
the torsatron Uragan-3M.
For H atoms, the energy dependences of the
reflection, re-emission coefficients and the total of these
coefficients were calculated in the energy range
3 eV…4 keV. For low-energy atoms, the total
coefficient increases from 0.26 to 0.41 in the range
3…10 eV. For high-energy CX atoms, this coefficient is
equal to 0.35 at energy of 120 eV, and 0.11 at energy of
4 keV (at the high-energy tail).
In prospect, the reflection and re-emission
coefficients are supposed to be used in the modeling of
the profiles of different particle parameters with the
code KN1D for the hydrogen plasma or for the near-
plasma region of the torsatron Uragan-3M.
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Article received 12.12.2016
КОЭФФИЦИЕНТЫ ОТРАЖЕНИЯ И РЕЭМИССИИ ВОДОРОДНЫХ ЧАСТИЦ, ПАДАЮЩИХ
ИЗ ПЛАЗМЫ НА СТЕНКУ В ТОРСАТРОНЕ УРАГАН-3М
В.Н. Бондаренко, А.А. Петрушеня
Моделирование радиальных профилей интенсивности линий Hα и Hβ, излучённых из водородной плазмы
торсатрона Ураган-3М в типичном рабочем режиме, требует использования программного кода KN1D для
рассмотрения баланса атомных и молекулярных потоков на стенках. С этой целью были вычислены
коэффициенты отражения и реэмисии атомов H и молекул H2, покидающих плазму и падающих на
обращённые к плазме поверхности кожухов винтовой обмотки из нержавеющей стали.
КОЕФІЦІЄНТИ ВІДБИТТЯ І РЕЕМІСІЇ ВОДНЕВИХ ЧАСТИНОК, ЩО ПАДАЮТЬ ІЗ ПЛАЗМИ
НА СТІНКУ В ТОРСАТРОНІ УРАГАН-3М
В.М. Бондаренко, А.А. Петрушеня
Моделювання радіальних профілів інтенсивності ліній Hα і Hβ, випромінених з водневої плазми
торсатрона Ураган-3М у типовому робочому режимі, вимагає використання програмного коду KN1D для
розгляду балансу атомних і молекулярних потоків на стінках. З цією метою були обчислені коефіцієнти
відбиття і реемісії атомів H і молекул H2, які покидають плазму і падають на повернені до плазми поверхні
кожухів гвинтової обмотки з нержавіючої сталі.
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