Impurity ion heating and drift velocity in the AL'FA experiment
High impurity ion energies (>100 eV) and toroidal drift velocities were reported in the early, ohmically heated experiment, Al'fa (Альфа, ~1960, major radius 1.6 m). These are explained here in terms of charged particle acceleration by the toroidal electric field corresponding to the noisy l...
Gespeichert in:
| Datum: | 2010 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2010
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/17459 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Impurity ion heating and drift velocity in the AL'FA experiment / D.H. McNeill // Вопросы атомной науки и техники. — 2010. — № 6. — С. 60-64. — Бібліогр.: 12 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-17459 |
|---|---|
| record_format |
dspace |
| spelling |
McNeill, D.H. 2011-02-26T20:59:30Z 2011-02-26T20:59:30Z 2010 Impurity ion heating and drift velocity in the AL'FA experiment / D.H. McNeill // Вопросы атомной науки и техники. — 2010. — № 6. — С. 60-64. — Бібліогр.: 12 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/17459 High impurity ion energies (>100 eV) and toroidal drift velocities were reported in the early, ohmically heated experiment, Al'fa (Альфа, ~1960, major radius 1.6 m). These are explained here in terms of charged particle acceleration by the toroidal electric field corresponding to the noisy loop voltage, using data from the experiment, atomic cross section data, and 1-D momentum equations without turbulence, radial fluxes, or microfield anomalies. In general, the impurities are thermally decoupled from the H (bulk) ions and electrons in the transiently runaway discharges. Высокие энергии (>100 эВ) и дрейфы примесных ионов обнаруживались в ранней установке с омическим нагревом "Альфа" (~1960 г., большой радиус 1.6 м). Результаты здесь объясняются ускорением заряженных частиц тороидальным электрическим полем, соответствующим шумному напряжению на оси шнура. Используются измерительные данные, информация об атомных сечениях и одноразмерные уравнения движения, не привлекая турбулентность, радиальные потоки, или аномалии микрополя. Вообще, ионы водорода и примесей (и электроны) термически развязаны в нестационарно убегающих разрядах. Високі енергії (>100 eВ) і дрейфи домішкових іонів виявлялися в ранній установці з омічним нагріванням "Альфа" (~1960 р., великий радіус 1.6 м). Результати тут порозуміваються прискоренням заряджених часток тороїдальним електричним полем, що відповідає шумовій напрузі на осі шнура. Використовуються вимірювальні дані, інформація про атомні перетини і однорозмірні рівняння руху, не залучаючи турбулентність, радіальні потоки, або аномалії мікрополя. Взагалі, іони водню і домішок (і електрони) термічно розв'язані в нестаціонарно втікаючих розрядах. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Фундаментальная физика плазмы Impurity ion heating and drift velocity in the AL'FA experiment Нагрев и дрейф примесных ионов в установке "АЛЬФА" Нагрівання і дрейф домішкових іонів в установці "АЛЬФА" Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Impurity ion heating and drift velocity in the AL'FA experiment |
| spellingShingle |
Impurity ion heating and drift velocity in the AL'FA experiment McNeill, D.H. Фундаментальная физика плазмы |
| title_short |
Impurity ion heating and drift velocity in the AL'FA experiment |
| title_full |
Impurity ion heating and drift velocity in the AL'FA experiment |
| title_fullStr |
Impurity ion heating and drift velocity in the AL'FA experiment |
| title_full_unstemmed |
Impurity ion heating and drift velocity in the AL'FA experiment |
| title_sort |
impurity ion heating and drift velocity in the al'fa experiment |
| author |
McNeill, D.H. |
| author_facet |
McNeill, D.H. |
| topic |
Фундаментальная физика плазмы |
| topic_facet |
Фундаментальная физика плазмы |
| publishDate |
2010 |
| language |
English |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Нагрев и дрейф примесных ионов в установке "АЛЬФА" Нагрівання і дрейф домішкових іонів в установці "АЛЬФА" |
| description |
High impurity ion energies (>100 eV) and toroidal drift velocities were reported in the early, ohmically heated experiment, Al'fa (Альфа, ~1960, major radius 1.6 m). These are explained here in terms of charged particle acceleration by the toroidal electric field corresponding to the noisy loop voltage, using data from the experiment, atomic cross section data, and 1-D momentum equations without turbulence, radial fluxes, or microfield anomalies. In general, the impurities are thermally decoupled from the H (bulk) ions and electrons in the transiently runaway discharges.
Высокие энергии (>100 эВ) и дрейфы примесных ионов обнаруживались в ранней установке с омическим нагревом "Альфа" (~1960 г., большой радиус 1.6 м). Результаты здесь объясняются ускорением заряженных частиц тороидальным электрическим полем, соответствующим шумному напряжению на оси шнура. Используются измерительные данные, информация об атомных сечениях и одноразмерные уравнения движения, не привлекая турбулентность, радиальные потоки, или аномалии микрополя. Вообще, ионы водорода и примесей (и электроны) термически развязаны в нестационарно убегающих разрядах.
Високі енергії (>100 eВ) і дрейфи домішкових іонів виявлялися в ранній установці з омічним нагріванням "Альфа" (~1960 р., великий радіус 1.6 м). Результати тут порозуміваються прискоренням заряджених часток тороїдальним електричним полем, що відповідає шумовій напрузі на осі шнура. Використовуються вимірювальні дані, інформація про атомні перетини і однорозмірні рівняння руху, не залучаючи турбулентність, радіальні потоки, або аномалії мікрополя. Взагалі, іони водню і домішок (і електрони) термічно розв'язані в нестаціонарно втікаючих розрядах.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/17459 |
| citation_txt |
Impurity ion heating and drift velocity in the AL'FA experiment / D.H. McNeill // Вопросы атомной науки и техники. — 2010. — № 6. — С. 60-64. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT mcneilldh impurityionheatinganddriftvelocityinthealfaexperiment AT mcneilldh nagrevidreifprimesnyhionovvustanovkealʹfa AT mcneilldh nagrívannâídreifdomíškovihíonívvustanovcíalʹfa |
| first_indexed |
2025-11-25T22:45:15Z |
| last_indexed |
2025-11-25T22:45:15Z |
| _version_ |
1850570916685152256 |
| fulltext |
BASIC PLASMA PHYSICS
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 6.
Series: Plasma Physics (16), p. 60-64.
Parameter Al'fa
(quiet phase)
Alcator-C Mod
IMPURITY ION HEATING AND DRIFT VELOCITY
IN THE AL'FA EXPERIMENT
D.H. McNeill
3955 Bigelow Blvd., Pittsburgh, PA 15213, USA
High impurity ion energies (>100 eV) and toroidal drift velocities were reported in the early, ohmically heated
experiment, Al'fa (Альфа, ~1960, major radius 1.6 m). These are explained here in terms of charged particle
acceleration by the toroidal electric field corresponding to the noisy loop voltage, using data from the experiment,
atomic cross section data, and 1-D momentum equations without turbulence, radial fluxes, or microfield anomalies. In
general, the impurities are thermally decoupled from the H (bulk) ions and electrons in the transiently runaway
discharges.
PACS: 52.20.-j, 52.30.-q, 52.70.-m, 52.55.-s
1. THE AL'FA EXPERIMENT
The Al'fa experiment, one of the earliest large nuclear
fusion experiments, was a diffuse toroidal pinch built at
the Physicotechnical Institute (FTI) in St. Petersburg
(Leningrad) in the late 1950's. Extensive diagnostic
development was done on Al'fa (spectroscopic,
microwave, bolometric, charge exchange, electrical, and
magnetic field measure-ments). The visible and near-UV
measurements, in particular, revealed the existence of
high ionization states of impurity ions (O, C, N) and
substantial toroidal drift velocities, parallel to the
discharge current, along with very high apparent
temperatures (far above the nominal electron temperature
Te) of these ions. Al'fa was modelled on and similar to the
British ZETA experiment [1-3]. The December 1960
issue of Zhurnal Tekhnicheskoi Fiziki (ЖТФ) was
devoted to articles on the construction, system
characteristics, and diagnostic results from Al'fa [4]. The
high drift velocity and, especially, the high apparent ion
temperatures in Al'fa have never received a satisfactory
explanation [1,2]. Here the spectroscopic results are
interpreted in a model that takes into account the
electrical behavior of the discharge, charged particle
acceleration in the toroidal electric field E, atomic cross
section data, the mechanics of elastic collisions, and
diagnostic response to these effects. The observed
impurity ion behavior can be explained in terms of the
production of high Z impurity ions by runaway electrons
generated during spikes in the loop voltage VL, the
average drift of the impurity ions in the average toroidal
electric field E of the discharge, and much faster drift in
the transient E corresponding to bipolar spikes in the very
noisy VL. This interpretation is consistent with the other
data from Al'fa. The best way of remembering that early
experiment is to interpret the diagnostic results from it
consistently and relate its physical behavior to modern
devices, such as reverse field pinches (RFP, of which
Al'fa is an ancestor) and tokamaks.
60
2. DIAGNOSTIC RESULTS
Many pioneering results from newly developed
diagnostic techniques, which are now in common use,
were reported for Al'fa [1,2,4]. The conclusions from that
time are qualitative by today's standards, but clearly
demonstrate the existence of collective plasma motions,
and fast, nonthermal populations of electrons, and
hydrogen and impurity ions.
The diagnostic techniques and results from Al'fa
include [4]: (i) Electrical and magnetic characteristics of
the discharge: condenser bank voltage, plasma loop
(induced) voltage VL, plasma current Ip, local magnetic
field B, and current density j. The nominal (quiescent,
average) current and loop voltage imply an electron
temperature Te=10-20 eV and an electron density
ne~1019 m-3. (ii) Fast H atoms with energies of several
keV were detected by a neutral energy analyzer, i.e., there
was a substantial tail in the proton energy distribution. (In
ZETA, neutrons from fusion of deuterium were detected.
The ions involved were found to be a suprathermal
streaming ion population). (iii) Spectroscopy (visible and
UV): high drift velocity and high apparent "temperatures"
of impurity ions (over 1 keV for OVI). The apparent
thermal speeds of the impurity ions (derived from the
observed line widths) were roughly 10 times their drift
velocities. (iv) Microwave diagnostics revealed the
existence of regions of plasma with densities above the
critical value for 8 mm (1.4·1019 cm-3) and collective
motion of the plasma at frequencies on the order of
105 Hz. (v) Bolometry (energy flux from plasma). The
basic measurements for Al'fa are summarized in Table 1.
Table 1. Comparison of the parameters of Al'fa [4] and
Alcator C-Mod (a currently operating tokamak) [5].
[The velocity ratio (*) refers to spectrum line half-half
width/line shift or thermal speed/drift speed]
major radius R [m] 1.6 0.67
minor radius a [m] 0.50 0.20
toroidal current I 150-350 kA 1.1 MA
toroidal B [T] 0.018-0.15 to 4.5
central elec. temp. Te(0) [eV] 10-20 ~1200 central ion temp. Ti(0) [eV] 10-20 (est.) ~1200
central elec. dens. ne(0) [m-3
] >1019 rising to ~2x1020
impurity ion charge Zx 2-5 (C, N, O) 17 (Ar)
loop voltage, quiescent VL [V] 400-1200 ~1
loop voltage, peak [V] -8000 to +8000 not known
toroidal E, quiescent [V/m] 20-500 ~0.2
drift velocity vd [m/s] ~1x104 (OV) -6x104 to -1x104
(early, late discharge)
vavg/vd * ~8 ~1 to 9
3. ELECTRICAL BEHAVIOR
L. A. Artsimovich, the developer of the tokamak,
described ([1], p. 254) traces of the plasma loop voltage
and current from the British ZETA experiment as
follows: "The first thing that strikes the eye on looking at
oscilloscope traces of the discharge is their complete
inconsistency with the notion of a 'quasistationary'
process. While the variation in I can, in a big stretch, be
regarded as comparatively smooth, the trace of V is
typical of a highly nonstationary process. The amplitude
of the high frequency voltage spikes is comparable to the
average voltage applied to the discharge chamber. The
characteristic frequency of these spikes is in the range
105…106 Hz."
Fig. 1. Oscilloscope traces of a discharge in the ZETA
experiment [1]: (1) current on the transformer primary,
(2) secondary (discharge) current I, (3) discharge (loop)
voltage VL, (4) dI/dt for the discharge current
The voltage spikes are bipolar relative to the
"average," filtered, or nominal value of VL. The measured
parameter for the plasma current Ip trace is actually the
(also) very noisy dIp/dt (Rogowsky loop signal), which is
integrated to yield the much smoother Ip(t). We shall
assume, as Artsimovich implies, that the amplitudes and
frequencies of the spikes in the Al'fa experiment, which
was based on ZETA, are similar.
In general, the loop voltage
VL=IR+d(LI)/dt, (1)
but in analyzing the Al'fa data [4], it was assumed that the
second term is negligible, i.e. VL=IR. In fact, the observed
(smoothed) I and VL traces and the plasma cross sectional
area are consistent [4] with Te=10…20 eV. In the Al'fa
discharge, however, d(LI)/dt= LdI/dt+IdL/dt is far larger
than IR, based on the time variation in dI/dt and VL. The
inductive terms can be large because of cutoff of all or
part of the plasma current (disruptions), whence
ΔVL=LηI/Δt for fixed L, a cutoff time Δt and a fraction η
of current loss, or because of periodic oscillations in the
plasma radius, a(t)=a0+asinωt, where the average radius
a0>>a, leaving dL/dt~4ω(a/a0)L0, where L0 is the average
L. The first mechanism is equivalent to the well-known
inductive kick of electronics [6] and is consistent with the
noisy dI/dt curve in Fig. 1, while the second is consistent
with the fluctuations in plasma radius observed by
microwave reflectometry in Al'fa. The time scales for
these fluctuations are on the order of 1…10 μs.
Both mechanisms can easily produce bipolar spikes about
the average VL with amplitudes 10 times that of the
average voltage.
4. PARTICLE DRIFTS IN AVERAGE E(t)
In order to explain the spectroscopic data, it is
necessary to abandon entirely the assumption of thermal
populations and evaluate the drifts of all charged particles
in the plasma in different phases of the discharge loop
voltage. For the nominal Te and ne the average toroidal
electric field E=VL/2πR, where R is the plasma major
radius, is close to the Dreicer limit Ec~0.2lnΛe/4πε0λD
2,
where λD=7.43x103(Te/ne)1/2 is the Debye length of the
plasma. This means that even in the quiescent phase, the
electrons are subject to runaway, but the (averge) drift
velocity (shift in the line centers) calculated from the
momentum equation for the impurity ions is close to the
observed values.
The spikes in VL imply a field far beyond the runaway
limit, and this, in turn, leads to two processes that are
fundamental to the observed spectroscopic results: (1)
production of electrons fast enough ionize the impurity
atoms to high degrees of ionization (CV, NV, OVI) and
excite the observed lines, and (2) acceleration of these
ions in the average and high transient fields to the
observed velocities. In this section, we discusss point (2)
for the average E(t), assuming the existence of highly
charged impurity ions; their origin (ionization by fast
electrons) and acceleration in the transient field is
discussed in the next section.
We begin with the average ("drift") velocity of these
ions in the average (quiescent) electric field.
In general, the 1-D (toroidal direction) equation for the
drift of plasma species α contains an electric field term
and a collisional drag term [7]
mα∂uα/∂t=ZαeE−Σβ≠α μαβναβ(uα−uβ), (2)
where ναβ is the momentum transfer rate in elastic
collisions (β is field species) and μαβ is the reduced mass
of particles α and β. All gradient and transverse terms are
neglected here. In the steady state, for the impurity ions
this equation yields
uX≈{ZXeE+μXeνXeue }/(μXAνXA)+ uA, (3)
i.e., the sum of an electric field force term and an electron
drag term, superimposed on the hydrogenic ion velocity.
In Al’fa, the electric field term dominates the drag on the
electrons and bulk ions, so that ion X has
uX≈ZXeE/(μXAνXA), (4)
parallel to the electric field. Given the current Ip, nominal
temperature (Te~10…20 eV), ne, ZX, average VL, and
plasma dimensions, this roughly yields the observed drift
velocities (up to 104 m/s parallel to Ip, for high Z) of the
various impurity ions in the average field E (cf. Fig. 2).
Table 2 lists the values of the force terms in Eq. (2) for
the average toroidal E in Al'fa [4] and L-mode ohmic
heating (OH) in Alcator [5] for O4+ and Ar17+ ions,
respectively. In the steady state, they yield uX parallel to
Ip in Al'fa and antiparallel to Ip in Alcator, as observed
[4,5], and as expected [8,9].
61
Table 2. Values of the terms in Eq. (2) for Al'fa and
Alcator C-Mod (O4+ and Ar17+ ions, respectively)
Al'fa {for range of
parameter}
Alcator-C Mod
ZxeE (N), electric field +(2.5-7.5)x10-17 {Vloop} +6.3x10-19
μxeνxe (kg/s) +(0.7-2)x10-22 {Te} +5.6x10-23
μxeνxeue (N), elec. drift -(2.0-5.7)x10-17 {Te, I} -1.5x10-17
μxiνxi (kg/s) +(0.4-1.2)x10-20 {Ti} +3.3x10-21
μxiνxiui (N), ion drift +9.2x10-19{T=10,I=.35 MA} +2.5x10-19
ux (m/s, direction
relative to Ip)
< 104,
positive
< 104,
negative
5. IONIZATION AND ACCLERATION
IN LOOP VOLTAGE SPIKES
The Dreicer runaway condition implies [7] that
electrons gain energy in accordance with the equation (no
collisional drag)
medve/dt≈ZeE=-eE. (5)
For a spike duration at constant field E (V/m) of Δt (s)
(square pulse), this implies a longitudinal velocity (drift)
of -eEΔt/me (m/s) at the end of the spike. Taking
E=VL/2πR, with VL=8000 and R=1.6 m, in a spike of
duration Δt=1-10 μs, we obtain
ve=1.76·1011EΔt~1.4·108 m/s → c. (6)
The corresponding electron kinetic energies can approach
hundreds of keV (limited by transverse drifts, e.g.,
curvature drift, inelastic collisions, relativistic effects, and
the particular shape of E(t)).
Similar free drift in the electric field takes place
among the plasma ions (Z≥1), as they experience little
electron drag. For fixed E and Δt, the velocity is
proportional to Z and the energy, to Z2. For O4+, the
velocity range for free acceleration in 1…10 μs spikes at
800 V/m ranges from ±1.9·104 m/s (as, above, within a
factor of ~ 2 of the observed average drift) to
±1.9·105 m/s, close to the nominal thermal speed derived
from the line shape of the OV line [4]. Therefore, the OV
ions have vOV=1.9·104 m/s average drift superimposed on
up to ±1.9·105 m/s during the rise and fall of the bipolar
current spikes. This yields symmetric profiles with a peak
corresponding to the mean-field drift (up to 104 m/s) and a
half-half width corresponding to the drift velocity
acquired in the spikes (up to 105 m/s). In general the line
shapes will not be gaussian, but the data are not good
enough to confirm that in any case.
62
Fig. 2. Averaged drift and spread (nominal Doppler half-
half width) of spectrum lines observed in Al'fa as
functions of ionic charge (Zaidel', [4])
The actual ion line profiles are determiend by the
projections of the velocity along the line of sight,
magnetic field curvature, and the time variation of E(t).
Deriving the line shape is a complicated problem of
plasma particle motions, instrument response, and
geometry.
The curves of Fig. 2 illustrate the range of impurity
ion drift velocities and nominal impurity temperatures
measured on Al’fa [4]. The averages and curve fits are not
definitive, as the quality of the data do not permit this and
the operating conditions at each point varied widely.
However, a nearly quadratic fit to the reported
TX(Z)∝vavg
2 and the linear fits to the velocities are
consistent with free acceleration in the average and
transient toroidal electric fields described here.
How do these highly ionized impurity ions show up in
an nominal Te=10 eV plasma? A transient runaway
electron population with energies >100 eV makes
multiple ionization of the background gas atoms possible.
Fig. 3 illustrates the species content and evolution
(accounting for the cumulative time to reach each
successive ionization state) of the oxygen ion population
for electron (equivalent) temperatures of 10 (mean), 30,
and 200 eV (runaway discharge during spikes), with
ne=1019 m-3 and ion lifetimes of 10 μs (fairly realistic,
corresponding to the transit time for neutral hydrogen
across the discharge and to the curvature drift motions of
the plasma column; also equal to the duration of the
longer spikes in VL) and 100 μs (comparable to the
discharge time of 1 ms and inelastic loss times, but much
longer than transverse drift times, etc.).
Fig. 3. Illustrating the time evolution of oxygen
ionization states in the average and transient phases of an
Al'fa discharge
Fig. 3 was obtained as follows: the density of ions in
state Z=i+1 is related to that in Z=i by
dni+1/dt=neni<σv>i– ni+1/τi+1– neni+1<σv>i+1, (7)
where ne, nk, and <σv>k are the electron density, density
in ion state Z=k, and electron impact ionization rate [10]
from state Z=k. τk represents the lifetime of ions in state k
(loss through transport, other inelastic processes, etc.). In
the steady state (long times) this becomes (assuming all
electrons locally at Te)
ni+1=ni<σv>i/(<σv>i+1+[neτi+1]-1). (8)
63
So, to get the above graph, begin with n0=1 (neutral
atoms) and the conditions Te, ne, and τk=t1 or t2 (assumed
same for all ions) indicated in the figure.
This shows that in the 10 eV discharges, the
populations of the OIII and higher ionization states are
very low for ion lifetimes of 10 μs. Even for a
unrealistically long lifetime of 100 μs, no significant
population of the higher states OIV and OV would be
detectable. On the other hand, with lifetimes of 10 μs or
less (corresponding to the VL spike durations) electrons
with energies (effective temperatures, as the electrons
cannot thermalize within 10 μs) of > 100 eV can easily
produce all the observed ion species of oxygen within a
few microseconds, i.e., within the duration of the voltage
spikes.
A more complete picture of the plasma state can be
obtained by examining the hierarchy of collision times in
the discharge phases (ταβ≡1/ναβ). For a Zeff ≥ 1.2 plasma
with a single impurity at Z ~ 3, temperatures ~ 10 eV, and
ne=1019 m-3, the major plasma species (hydrogen,
electrons, impurity ion) are in equilibrium and all
momentum collision times are ≤10 μs, with all energy
collision times shorter than the discharge lifetime of
~1 ms.
If we assume particle energies (effective temperatures)
of ~1 keV, the energy collision times [7] all exceed 10 ms
or ten times the discharge duration (except e-e, for which
τee
E~10 μs). Of the momentum collision times, only the
electron field produces a collision time less than 100 μs,
so the heavy particle drifts are thoroughly decoupled in
the sense described above (in terms of the momentum
equation).
6. SUMMARY AND CONCLUSIONS
Extraordinarily high impurity ion temperatures and
substantial toroidal drift of these ions, detected by visible
and near-UV spectroscopy, were reported for the Al'fa
experiment. The reported temperatures have always been
something of a mystery, for, at the nominal Te=10 eV and
ne=1019 m-3, these ion states (up to Z=5) cannot form in
the plasma during its lifetime (1 ms), much less within the
shorter transport, transverse drift, and inelastic collisional
loss times.
As in the case of OH tokamaks [8], the observed
toroidal drift velocities can be derived from the average
(smoothed) loop voltage VL and discharge current using
the momentum equations, but in Al'fa the electric field
term dominates, leading to drift in the direction of the
plasma current Ip (or toroidal electric field E). The
average VL implies a toroidal electric field close to the
Dreicer limit for electron runaway in Al'fa. This is rarely
the case in the main discharge phase of modern OH
tokamaks, where VL is low and relatively quiescent, so
that the impurity drifts are opposite to the direction of
toroidal current (field), i.e., parallel to the electron drift.
The key to the high ion “temperatures” in Al'fa lies in
the noisy loop voltage (confirmed by the noisy dI/dt
signal), with bipolar excursions to 10 times the average
value readily calculable using the measured electrical and
plasma parameters. In this case, I = IR+d(LI)/dt ~
d(LI)/dt>>IR. The loop voltage spikes could be produced
by the term I(dL/dt), i.e., by changes in the plasma
configuration, or by L(dI/dt), i.e., by cutoff of all or part
of the plasma current (inductive kick). These events occur
on time scales of 1…10 μs – the time scales of the
observed spikes in VL, as well as, e.g., for curvature drift
out of the plasma column.
These transient voltage spikes imply high electric
fields – sufficient to accelerate all ion species as well as
electrons in a runaway (no collisional drag) regime;
particle losses can occur through transverse drifts,
inelastic processes, etc. Electrons may be thermalized,
but not the hydrogenic or impurity ions. The resulting
electron energies are sufficient to ionize the O, N, and C
impurities (within 1…10 μs, in sequence) to the observed
ionization states.
These multiply charged ions are then accelerated, in
both directions, by the field corresponding to the bipolar
spikes in VL to the velocities observed in the experiments.
The velocity is higher for higher ionic charges, roughly
consistent with an ion energy KΖ∝Ζ2, as in free
acceleration in an electric field with little or no collisional
drag (other losses limit the ion velocity/energy).
The magnitudes of the velocities of the impurity ions
in the average and peak electric fields are sufficient to
explain the apparent spectroscopically observed
"temperature" of the impurity ions in Al'fa. (The wings of
the observed spectral lines correspond to the high field
drift when these ions exist during the voltage spikes and
the average shift of the line profile corresponds to the drift
produced in the average electric field.)
The model used here to interpret the spectroscopic
observations involves 3 stages of modelling: (1) electrical
characteristics of the discharge (VL~d(LI)/dt>>IR), (2)
acceleration of electrons in the high, transient E field
leading to ionization of impurity species, and (3)
acceleration of impurity ions in the average and transient
electric fields
The spectroscopic and electrical observations on Al'fa
are consistent with other data obtained from the device,
including charge exchange detectors (fast hydrogen
neutrals), microwave reflectometry (fluctuations in
plasma position/size and density – as the impurity atoms
become multiply ionized there should be a rapid rise in
the local ne), bolometry, and (in ZETA) production of
nonthermal neutrons from deuterium (through collisions
of fast deuterium ions with walls and in the vessel
volume, spallation, etc.). It is noteworthy that a smaller
British pinch, Sceptre IV, [11] and, later, ZETA, were
operated in a quiescent mode that yielded lower impurity
ion (OV) "temperatures," consistent with the present
model. Impurity ion drift dominated by the toroidal
electric field term (cf. Eq. (3)) may apply to other
ohmically heated toroidal devices with high VL, such as
RFPs which are a descendent of Al'fa and ZETA [12],
and, possibly, some early tokamak experiments in which
the loop voltage was relatively high throughout the
discharge.
REFERENCES
1. L.A. Artsimovich. Управляемые термоядерные
реакции (Controlled Thermonuclear Reactions).
Moscow: “Atomizdat”/ 2nd ed. 1963.
64
2. S.Yu. Luk'yanov. Горячая плазма и управляемый
ядерный синтез (Hot Plasmas and Controlled
Thermonuclear Fusion). Moscow: “Nauka”, 1975.
3. G. N. Harding et al.// Proc. 2nd Geneva Conf. on the
Peaceful Uses of Atomic Energy. 1958, v. 32, p. 365-
378.
4. V.V. Afrosimov, et al.// Zhurnal Tekhnicheskoi Fiziki
(ЖТФ). 1960, v. 30, N 12, p. 1381-1488.
5. J. E. Rice, et al.// Nucl. Fus. 1997, v. 37, p. 421.
6. Kenneth L. Kaiser. Electronic Compatibility Handbook.
CRC Press, 2005.
7. V.E. Golant, et al. Fondamenti di fisica dei plasmi
(Основы физики плазмы). Moscow: “Edizioni Mir”,
1983.
8. D.H. McNeill. Impurity ion drift and toroidal rotation
in tokamaks // Problems of Atomic Science and
Technology. Series “Plasma Phisics”(16). 2010, N6,
p. 65 (in this N).
9. D.H. McNeill // 33rd European Phys. Soc. Conf. on
Plasma Physics. Rome, 2006. Paper P4.182.
10. K.L. Bell, et al. Atomic and Molecular Data for
Fusion. Part I: Report CLM-R216, Culham
Laboratory, UK, 1981.
11. N. L. Allen // J. Nucl. Energy C. 1962, p. 375.
12. R. J. Bickerton // Phil. Trans. R. Soc. Lond. A. 1999,
v. 357, p. 397-413.
Article received 13.09.10
НАГРЕВ И ДРЕЙФ ПРИМЕСНЫХ ИОНОВ В УСТАНОВКЕ "АЛЬФА"
Д.Х. Макнилл
Высокие энергии (>100 эВ) и дрейфы примесных ионов обнаруживались в ранней установке с омическим
нагревом "Альфа" (~1960 г., большой радиус 1.6 м). Результаты здесь объясняются ускорением заряженных
частиц тороидальным электрическим полем, соответствующим шумному напряжению на оси шнура.
Используются измерительные данные, информация об атомных сечениях и одноразмерные уравнения
движения, не привлекая турбулентность, радиальные потоки, или аномалии микрополя. Вообще, ионы
водорода и примесей (и электроны) термически развязаны в нестационарно убегающих разрядах.
НАГРІВАННЯ І ДРЕЙФ ДОМІШКОВИХ ІОНІВ В УСТАНОВЦІ "АЛЬФА"
Д.Х. Макнілл
Високі енергії (>100 eВ) і дрейфи домішкових іонів виявлялися в ранній установці з омічним нагріванням
"Альфа" (~1960 р., великий радіус 1.6 м). Результати тут порозуміваються прискоренням заряджених часток
тороїдальним електричним полем, що відповідає шумовій напрузі на осі шнура. Використовуються
вимірювальні дані, інформація про атомні перетини і однорозмірні рівняння руху, не залучаючи
турбулентність, радіальні потоки, або аномалії мікрополя. Взагалі, іони водню і домішок (і електрони) термічно
розв'язані в нестаціонарно втікаючих розрядах.
|