Distribution functions of secondary runaway electrons
The review of different shapes of runaway electron secondary generation distribution functions are presented. Conditions which lead to different shapes of these functions are considered.
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2000 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Cite this: | Distribution functions of secondary runaway electrons / I.M. Pankratov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 58-59. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859752010553753600 |
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| author | Pankratov, I.M. |
| author_facet | Pankratov, I.M. |
| citation_txt | Distribution functions of secondary runaway electrons / I.M. Pankratov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 58-59. — Бібліогр.: 14 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The review of different shapes of runaway electron secondary generation distribution functions are presented. Conditions which lead to different shapes of these functions are considered.
|
| first_indexed | 2025-12-02T00:13:41Z |
| format | Article |
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UDC 533.9
58 Problems of Atomic Science and Technology. 2000. № 6. Series: Plasma Physics (6). p. 58-59
Distribution functions of secondary runaway electrons
I.M. Pankratov
Institute of Plasma Physics, NSC 'Kharkov Institute of Physics and Technology',
Academicheskaya 1, 61108 Kharkov, Ukraine
The review of different shapes of runaway electron secondary generation distribution functions are presented.
Conditions which lead to different shapes of these functions are considered.
1. INTRODUCTION
The secondary generation of runaway electrons is a
fundamental phenomenon. Secondary generation is a
process in which already existing high-energy runaway
electrons (of the order of 10 MeV or large) kick thermal
electrons into the runaway region by close Coulomb
collisions (see, e.g., [1]). The knocked out electrons
have a significant transverse momentum p⊥ >> p// (p⊥
and p// are the transverse and parallel momenta of the
runaways with respect to the magnetic field B). The
inequality )4/( 2
0
32 ELmnep ecr πε=
crpp ⊥⊥ > , (1)
where
3/2124 +≈⊥ effcrcr Zpp
determines the runaway region of the knocked out
electrons [2], e and m are the charge and rest mass of
electrons, ne the bulk electron density, L the Coulomb
logarithm, Zeff the effective ion charge and E the
inductive electric field. The knocked out electrons run
away in the electric field and in turn make more
runaways. The avalanche-like process of runaway
generation arises with the avalanching time [3] (c the
velocity of light)
eEZmcLEt eff 9/)2(12)(0 += (2)
Runaway avalanches generated during disruptions in
large tokamaks like ITER may have damaging
consequences because of the high power generated by
their localized deposition on the vessel walls [4].
In the same time the established methods of
monitoring the presence of runaway electrons (HXR,
photoneutron emission) will be difficult to apply in
large machines like ITER because of the high gamma
and neutron background and the very thick wall and in
vessel shielding thickness. Only the diagnostic based on
the runaway electron synchrotron radiation
measurements should be possible on ITER [4].
The analysis of the runaway electron distribution
function is very important for the understanding of the
runaway avalanche formation and for the correct
interpretation of synchrotron radiation diagnostic data.
That is the reason why the review of investigations of
secondary runaway electron distribution functions
),,(2),(
0
//// tppfdpptpf ∫
∞
⊥⊥⊥= π (3)
are presented in this paper.
2. STEADY STATE PLASMA
For steady state conditions, when plasma parameters
ne, Zeff, E are not changed, the calculations were made
on the basis of the integral of close collisions [2]. We
assumed that runaways had parallel momenta p// up to
the maximum value p// max. And the time tconf was the
time over which an electron undergoes a change in
parallel momentum p// from a value close to pcr to a
maximum value p//max.
In the case when avalanching time t0 (2) was larger
than the confinement time (t0 > tconf) the distribution
function of secondary runaways went over to a
stationary value [2]. This function had a large peak in
region where p// was less or of the order of pcr and a flat
distribution outside this region (up to p//max). In this
situation the avalanching process was suppressed: the
density of runaways also went over to a stationary value
[5].
In the case when avalanching time t0 was less than
the confinement time (t0 < tconf) the distribution function
),( // tpf had an exponentially decaying dependence on
the parallel momentum [3]. Again a large peak was in
the region where p// was less or of the order of pcr.
These calculations were carried out for the TEXTOR
experimental conditions [6]. In this experiment the
secondary runaway generation was first demonstrated.
Few years ago TEXTOR experiments were carried
out with the aim of the control of runaway electron
secondary generation by changing Zeff [7]. Different
amplitudes of neon gas puffs were injected during
steady state phases of low density ohmic deuterium
discharges in which the runaway electron secondary
generation process took place.
In the flat top phase of the discharge an exponential
increase of the synchrotron radiation in time was the
indication of the avalanching of the runaway electron
population with energies higher 15 MeV. With a time
detay ∆t = 0.6 – 0.75s after start of neon puff the
synchrotron radiation signal showed a sufficiently sharp
transition from the fast avalanching process to a decay
or more slow avalanching processes.
59
During neon injection the parameter p⊥ ,cr was
increased because of Zeff increase. And from the
injection time the number of knocked out electron (and
hence ),( // tpf ) was decreased in the region where p
was of the order or less than pcr. The time of delay ∆t is
the time over which an electron underwent a change in
parallel momentum p// from a value close to pcr to
relativistic value of p//. From this moment, the
synchrotron signal showed a transition to the new
regima. In this experiments the evolution of
),( // tpf took place as it was shown in Fig. 5 of Ref.
[7]. Recent TEXTOR experiment [8] also confirmed
this interpretation.
3. DISRUPTIONS
During disruptions at the plasma centre the
inductive toroidal electric field E strongly changes from
values of E ~ (0.1-0.05) V/m up to E ~ (50-100) V/m
and then it drops to the typical value of E ~ 5V/m (see,
e.g., [9, 10, 11]). The plasma parameters ne and Zeff also
change but not so strong.
The evolution of the runaway parameters strongly
influences the avalanching process. During the time
when E is very high the parameter p⊥ cr Eq. (1) is small.
The strong runaway avalanche takes place. The
exponentially decaying dependence of distribution
),( // tpf on the momentum //p (with a huge peak at low
energies) occurs.
When E strongly (> 10 times) drops, the parameter
p⊥ cr strongly increases. The production rate of the
secondary generation decreases, a large peak in the
knocked out electron distribution function at low
energies is now below the runaway region. The
enhancement of superthermal electron losses from low
energy region arises. The runaway avalanche is reduced.
In this stage of disruption the function ),( // tpf has a
gap in the region p ~ p cr . And this gap extends from p ~
p cr to larger values of p//.
Note that only exponentially decaying dependence
of a distribution function on the parallel momentum was
considered in Refs. [12, 13].
For the situations reported here the inequality
22
0
3 4/ mcLneE e πε>> (4)
holds, indicating the possibility of runaway generation
[14].
4. CONCLUSIONS
The evolution of the plasma parameters and runaway
losses lead to different dependences of runaway electron
secondary generation distribution function on the
parallel momentum p//: an exponentially decaying
distributions, flat distributions and distributions with a
gap in the region p ~ p cr .
REFERENCES
1. I.M. Pankratov, R. Jaspers, K.H. Finken et al.,
Proc. 26th EPS Conf. on Contr. Fusion and Plasma
Physics (Maastricht, 1999), Vol. 23J, p. 597.
2. N.T. Besedin, I.M. Pankratov, Nucl. Fusion 26
(1986) 807.
3. I.M. Pankratov, N.T. Besedin, Proc 23rd EPS Conf.
on Contr. Fusion and Plasma Physics (Kiev, 1996),
Vol. 20C, Part I, p. 279.
4. ITER Physics Basis, Nucl. Fusion 39 (1999),
No. 12.
5. N.T. Besedin, Yu. K. Kuznetsov, I.M. Pankratov,
Sov. J. Plasma Phys. 12 (1986) 436.
6. R. Jaspers, K.H. Finken, G. Mank et al., Nucl.
Fusion 33 (1993) 1775.
7. I.M. Pankratov, R. Jaspers, K.H. Finken et al.,
Nucl. Fusion 38 (1998) 279.
8. V.S. Udintsev, R. Jaspers, A.J.H.Donne et al.,
Proc. 27th EPS Conf. on Contr. Fusion and Plasma
Physics (Budapest, 2000), P3.028.
9. R.D. Gill, B. Alper, A.W. Edwards et al., Nucl.
Fusion 40 (2000) 163.
10. I. Senda, T. Shoji, T. Tsunematsu et al., Fusion
Engineering and Design 45 (1999) 15.
11. R. Jaspers, I.M. Pankratov, K.H. Finken et al., Proc.
25th EPS Conf. on Contr. Fusion and Plasma Phys.,
Praha, 1998, Vol. 22C, 683.
12. R. Jayakumar, H.H. Fleischmann, S.J. Zweben,
Phys. Letters A172 (1993) 447.
13. S.C. Chiu, M.N. Rosenbluth, R.W. Harvey et al.,
Nucl. Fusion 38 (1998) 1711.
14. J.W. Connor, R.J. Hastie, Nucl. Fusion 15 (1975)
415.
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| id | nasplib_isofts_kiev_ua-123456789-78498 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-02T00:13:41Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Pankratov, I.M. 2015-03-18T16:24:20Z 2015-03-18T16:24:20Z 2000 Distribution functions of secondary runaway electrons / I.M. Pankratov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 58-59. — Бібліогр.: 14 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/78498 533.9 The review of different shapes of runaway electron secondary generation distribution functions are presented. Conditions which lead to different shapes of these functions are considered. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Distribution functions of secondary runaway electrons Article published earlier |
| spellingShingle | Distribution functions of secondary runaway electrons Pankratov, I.M. Magnetic confinement |
| title | Distribution functions of secondary runaway electrons |
| title_full | Distribution functions of secondary runaway electrons |
| title_fullStr | Distribution functions of secondary runaway electrons |
| title_full_unstemmed | Distribution functions of secondary runaway electrons |
| title_short | Distribution functions of secondary runaway electrons |
| title_sort | distribution functions of secondary runaway electrons |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78498 |
| work_keys_str_mv | AT pankratovim distributionfunctionsofsecondaryrunawayelectrons |