Disruption generated secondary runaway electrons in present day tokamaks
An analysis of the runaway electron secondary generation during disruptions in present day tokamaks (JET, JT- 60U, TEXTOR) was made. It was shown that even for tokamaks with the plasma current I ~ 100 kA the secondary generation may dominate the runaway production during disruptions. In the same tim...
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irk-123456789-823642015-05-30T03:01:35Z Disruption generated secondary runaway electrons in present day tokamaks Pankratov, I.M. Jaspers, R. Мagnetic Confinement An analysis of the runaway electron secondary generation during disruptions in present day tokamaks (JET, JT- 60U, TEXTOR) was made. It was shown that even for tokamaks with the plasma current I ~ 100 kA the secondary generation may dominate the runaway production during disruptions. In the same time in tokamaks with I ~ 1 MA the runaway electron secondary generation during disruptions may be suppressed. 2000 Article Disruption generated secondary runaway electrons in present day tokamaks / I.M. Pankratov, R. Jaspers// Вопросы атомной науки и техники. — 2000. — № 3. — С. 39-41. — Бібліогр.: 11 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/82364 533.9 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Мagnetic Confinement Мagnetic Confinement |
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Мagnetic Confinement Мagnetic Confinement Pankratov, I.M. Jaspers, R. Disruption generated secondary runaway electrons in present day tokamaks Вопросы атомной науки и техники |
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An analysis of the runaway electron secondary generation during disruptions in present day tokamaks (JET, JT- 60U, TEXTOR) was made. It was shown that even for tokamaks with the plasma current I ~ 100 kA the secondary generation may dominate the runaway production during disruptions. In the same time in tokamaks with I ~ 1 MA the runaway electron secondary generation during disruptions may be suppressed. |
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Article |
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Pankratov, I.M. Jaspers, R. |
| author_facet |
Pankratov, I.M. Jaspers, R. |
| author_sort |
Pankratov, I.M. |
| title |
Disruption generated secondary runaway electrons in present day tokamaks |
| title_short |
Disruption generated secondary runaway electrons in present day tokamaks |
| title_full |
Disruption generated secondary runaway electrons in present day tokamaks |
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Disruption generated secondary runaway electrons in present day tokamaks |
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Disruption generated secondary runaway electrons in present day tokamaks |
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disruption generated secondary runaway electrons in present day tokamaks |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2000 |
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Мagnetic Confinement |
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http://dspace.nbuv.gov.ua/handle/123456789/82364 |
| citation_txt |
Disruption generated secondary runaway electrons in present day tokamaks / I.M. Pankratov, R. Jaspers// Вопросы атомной науки и техники. — 2000. — № 3. — С. 39-41. — Бібліогр.: 11 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT pankratovim disruptiongeneratedsecondaryrunawayelectronsinpresentdaytokamaks AT jaspersr disruptiongeneratedsecondaryrunawayelectronsinpresentdaytokamaks |
| first_indexed |
2025-07-06T08:52:14Z |
| last_indexed |
2025-07-06T08:52:14Z |
| _version_ |
1836886980613373952 |
| fulltext |
UDC 533.9
Problems of Atomic Science and Technology. 2000. N 3. Series: Plasma Physics (5). p. 39-41 39
Disruption generated secondary runaway electrons
in present day tokamaks
I.M. Pankratov1, R. Jaspers2
1Institute of Plasma Physics, NSC 'Kharkov Institute of Physics and Technology',
Academicheskaya 1, 61108 Kharkov, Ukraine
2FOM-Instituut voor Plasmafysica ´Rijnhuizen´, Association EURATOM-FOM,
P.O.Box 1207, 3430 BE Nieuwegein, The Netherlands*
An analysis of the runaway electron secondary generation during disruptions in present day tokamaks (JET, JT-
60U, TEXTOR) was made. It was shown that even for tokamaks with the plasma current I ∼ 100 kA the secondary
generation may dominate the runaway production during disruptions. In the same time in tokamaks with I ∼ 1 MA
the runaway electron secondary generation during disruptions may be suppressed.
* Partner in the Trilateral Euregio Cluster
1. INTRODUCTION
One of the important problems of a tokamak fusion
reactor is the possible damage caused by disruption
generated runaway electrons. The avalanching process
of runaway electron secondary generation was
recognized to dominate the runaway production during
major disruptions in large tokamaks like ITER [1]. But
for present day tokamaks the role of the runaway
electron secondary generation during disruptions is
under discussion up to now. That is the reason why this
paper is presented.
Remind that the secondary generation is the process
in which already existing high energy runaway electrons
kick thermal electrons into the runaway region by close
Coulomb collisions.
2. RUNAWAY GENERATION
The importance of the runaway electron secondary
generation in a disruption can be investigated on the
base of two equations.
The inductive toroidal electric field E(t) at the center
of the plasma is given by
dt
dÔ
R
tE
2
1
)(
π
−= , (1)
where
∫=)(tÔ BdS (2)
is the magnetic flux across the surface bounded by the
circular contour with radius R, R is the major radius of
the runaway beam center. Note, that experiments show
that the runaways are generated at the plasma center in a
region with small minor radius (see, e.g., [2]).
The runaway production is given by [2]
l
rr
ee
r tn
Et
tn
tttn
dt
dn
τ
λν )(
)(
)(
)()()(
0
−+= (3)
The first term in the right side of Eq. (3) describes
the primary (Dreicer) generation (see, e.g., [3]). Here
nr(t) is the density of runaways,
(t),E(t)/Eå (t)
,vmðå(t)Lnev
D
ee
=
= 322
0
4 4/
(4)
åZ (Z
eff
effeff e)åK(Zë(t)
)/1(4/116)/13 +−−+−= å
, (5)
)(tne - is the bulk plasma density, e, m and v are the
charge and the rest mass and the velocity of the
electron, L is the Coulomb logarithm, Zeff is the
effective ion charge number, ED(t) = e 3ne(t)L/4πε0
2Te(t),
Te – is the bulk electron temperature, K(Zeff) is a weak
function of Zeff (K(1) = 0.32, K(2) =0.43).
The second term in the right side of Eq.(3) describes
the secondary generation with the avalanching time [4]
(c the velocity of light)
eEZmcLEt eff 9/)2(12)(0 += (6)
The last term in the right side of Eq. (3) describes
the losses of runaways.
From Eqs. (1), (3) we obtain the runaway current
density jr(t) = ecnr(t) (t = 0 is the start of the runaway
generation)
],/)(exp[)0(]}/)(exp[)(
)()({)]/)((exp[)(
0
lrle
e
t
lr
ttsjttstn
ttdtttsectj
ττ
λντ
−∆++
∫+−=
(7)
where
R
tÔ
ZmcL
e
ts
eff π2
)(
)2(2
33
)(
+
= , (8)
)()0()( tssts −=∆ (9)
Problems of Atomic Science and Technology. 2000. N 3. Series: Plasma Physics (5). p. 39-41 40
The second term in Eq.(7) describes the secondary
generation of runaway electrons, the necessary
condition of this process is
0)( >∆ ts (10)
Or in the more suitable form (IA = 0.017MA is the
Alfven current):
0)]()()0()0([
1
2
6.2
)]()()0()0([
2
1
2
6.2
>−
+
=
=−
+
≈∆
thtIhI
LIZ
tLtILI
RmcL
e
Z
s
ii
Aeff
ôÔ
eff π
(11)
We introduce the flux inductance of the plasma
current I(t) (see, e.g., [5]),
Ô = LôI, (12)
where
Lô = µ0Rhi /2 , (13)
hi is the normalized flux inductance of the plasma
column. Note that hi differs from the normalized energy
self inductance li. In Eq. (11) the evolution of the
current density profile during disruptions is taken into
account.
To estimate the value of hi we consider the simple
model of the current density profile j(r)
j(r) = j1, r < rc , (14)
j(r) = j2, rc < r <rp , (15)
where rc is the minor radius of the central part of a
plasma, rp is the minor plasma radius (rc
2 << rp
2 ), I1
= π rc
2 j1 is the current in the central part of a plasma, I2
= π (rp
2 - rc
2)j2 is the current outside the plasma center.
Using Eqs. (2), (12) – (15) we find that
)(
)/ln(2
1
22
2
2
1
21 cp
ccp
i
rr
rI
I
II
rr
h
−
−
+
+= (16)
If j1 = j2 from Eq. (16) we have hi = 1. In the case
I1 >> I2
)/ln(21 cpi rrh +≈ (17)
Note, that the value of the normalized energy self
inductance li for our simple model of the current density
profile Eqs. (14), (15) is given by
)]
5.0
(4
ln)(4[
)(
5.0
22
2
2
12
2
22
2
2
1
2
2
2
12
21
cp
c
c
p
cp
c
i
rr
rI
II
r
r
rr
rI
III
II
l
−
−+
+
−
−++
+
=
(18)
If j1 = j2 f rom Eq. (18) we have li = 0.5. In the case
I1 >> I2
)/ln(25.0 cpi rrl +≈ (19)
3. DISCUSSION
In this section we estimate the role of the runaway
electron secondary generation during disruptions in
JET, TEXTOR and JT-60U tokamaks.
In JET the density limit disruption # 42155 [6] had
all the usual disruption characteristics such as the
negative voltage spike and therefore a flat current
profile may be assumed in the initial current quench
phase. The runaway generation was observed after a
small delay of (4-6) ms after the thermal quench (I(0) ≈
1,5 MA), the runaway beam was located in the central
part of a plasma with the radius of the runaway beam
rbeam ≈ 15 cm (rp ≈ 1m). In the current plateau stage the
runaway current was Irun(t) ≈ 0.6 MA (I(t) ≈ 1MA) and
rbeam ≈ 0.3 m.
At the start of runaway generation (t = 0) rc ≈ 0.2 m
and I2 > I1, hence hi (0) ≈ 2.5. In the plateau stage rc
≈ 0.35m and I2 ≅ I1, hence hi (t) ≈ 2. Note that the value
hi ≈ 2 - 2.5 is in good agreement with Lô = 4.5 µH
of Ref. [5]. For ∆s (L = 12; Zeff = 3) we have
approximately
∆s ≅ 4.5.
This estimate is in good agreement with calculation of
Ref. [7].
The TEXTOR disruption # 55860 [2, 8] was a result
of a huge gas puff in a low density discharge. Contrary
to usual disruptions no negative voltage spike was
observed in the thermal quench and a flattening of the
current profile did not occur. After a delay (4-6)ms after
the thermal quench (I(0) ≈ 100 kA) a strong runaway
generation in the central part of the plasma started. The
rbeam ≈ (5-7)cm was small compared to the plasma minor
radius rbeam = 46 cm. The runaway current was Ir ≈ (20-
30)kA about 30% of the total current in the plasma I(t)
≈ 75kA when the runaway plateau is formed.
In this shot at the start of runaway generation a
strongly peaked current profile took place: I1 >> I2 , rc ≈
≈ 0.1 m and hence hi(0) ≈ 4. In the plateau stage I2 > I1
(rc ≈ 0.1m) and hi(t) ≈ 2. For ∆s we have from Eq. (11)
(L = 10, Zeff = 3)
∆s ≈ 0.75.
This estimate shows that even for tokamaks with
I ~ 0.1 MA secondary generation can dominate the
runaway production during disruption.
The investigation of the runaway generation during
disruptions in JT-60U (see, e.g., [9]) shows that the
secondary generatuon process does not play the
principal role here. In the same time in these
experiments a very high value of the plasma internal
energy unductance li ≈ 3,5 (and hence hi ≈ 4), was
observed. It means that the last term in Eq. (11)is large
for this case and it was the reason (in addition to a high
level of magnetic perturbations) why the runaway
avalanches were suppresed during disruptions in
JT-60U.
Problems of Atomic Science and Technology. 2000. N 3. Series: Plasma Physics (5). p. 39-41 41
It is necessary to underline that in all considered
here disruptions the strong inequality [10]:
22
0
3 4/ mcLneE e πε>> (20)
holds, indicating the possibility for runaway generation.
4. CONCLUSIONS
Up to now to estimate the role of runaway electron
secondary generation during disruptions in tokamaks the
next expression [11] was used
LIIt ARA /≅γ (21)
From Eq. (21) it is possible to wait the strong
runaway avalanche in JT-60U and no avalanche in
TEXTOR disruptions. But experiments show that these
conclusions are not correct.
As it is shown in the present paper that for the
correct analysis of runaway avalanches during
disruptions it is necessary to take into account not only
the plasma current value, but also the evolution of the
current density profile.
ACKNOWLEDGEMENTS
The authors are grateful to Dr. T. Dolan for useful
discussion.
REFERENCES
1. ITER Physics Basis, Nucl. Fusion 39 (1999),
No.12.
2. R. Jaspers, N.J. Lopes Cardozo, F.C. Schüller et
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3. V.V. Parail, O.P. Pogutse, Runaway Electrons in a
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by M.A. Leontovich, Consultants Bureau, New
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