Stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor is observed numerically for the first time. This validates theory prediction that the collisionless stochastic diffusion of these particles represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators [Beidler et al., Phys. Plasmas 8, 2731 (2001)]. The numerical calculation has also demonstrated a possibility to prevent the escape of particles to the wall by making the separatrix between the locally trapped and passing states closed, as was proposed in Tykhyy et al. [Plasma Phys. Control. Fusion 49, 703 (2007)]. It is found that stochastic regions can vary from very narrow to very wide that occupy almost the whole plasma cross section. It is shown that the fraction of alpha particles with closed separatrix in the population of transition alphas can be considerable. Potentially, this fraction can be increased, and the number of transitioning particles can be reduced by a special optimization of the magnetic configuration, which decreases delayed losses of alphas by means of reducing the separatrix maximum radius.

1.
P.
Helander
,
Rep. Prog. Phys.
77
,
087001
(
2014
).
2.
H.
Wobig
,
T.
Andreeva
,
C. D.
Beidler
,
E.
Harmeyer
,
F.
Herrnegger
,
Y.
Igitkhanov
,
J.
Kisslinger
,
Y. I.
Kolesnichenko
,
V. V.
Lutsenko
,
V. S.
Marchenko
,
C.
Nührenberg
,
I.
Sidorenko
,
Y.
Turkin
,
A.
Wieczorek
, and
Y. V.
Yakovenko
,
Nucl. Fusion
43
,
889
(
2003
).
3.
W.
Lotz
,
P.
Merkel
,
J.
Nührenberg
, and
E.
Strumberger
,
Plasma Phys. Controlled Fusion
34
,
1037
(
1992
).
4.
M.
Drevlak
,
J.
Geiger
,
P.
Helander
, and
Y.
Turkin
,
Nucl. Fusion
54
,
073002
(
2014
).
5.
C. D.
Beidler
,
Y. I.
Kolesnichenko
,
V. S.
Marchenko
,
I. N.
Sidorenko
, and
H.
Wobig
,
Phys. Plasmas
8
,
2731
(
2001
).
6.
A. V.
Tykhyy
,
Ukr. J. Phys.
63
,
495
(
2018
).
7.
A. J.
Lichtenberg
and
M. A.
Lieberman
,
Regular and Stochastic Motion
(
Springer
,
New York
,
1983
).
8.
J.
Lamperti
,
Stochastic Processes: A Survey of the Mathematical Theory
(
Springer
,
New York
,
1977
).
9.
E.
Ott
,
Chaos in Dynamical Systems
(
Cambridge University Press
,
New York
,
1993
).
10.
A. V.
Timofeev
,
Sov. Phys. JETP
48
,
656
(
1978
).
11.
A. I.
Neishtadt
,
Sov. J. Plasma Phys.
12
,
568
(
1986
).
12.
J. R.
Cary
,
D. F.
Escande
, and
J. L.
Tennyson
,
Phys. Rev. A
34
,
4256
(
1986
).
13.
D. L.
Bruhwiler
and
J. R.
Cary
,
Phys. D
40
,
265
(
1989
).
14.
J. R.
Cary
and
R. T.
Skodje
,
Phys. D
36
,
287
(
1989
).
15.
D. L.
Vainshtein
,
A. A.
Vasiliev
, and
A. I.
Neishtadt
,
Chaos
6
,
514
(
1996
).
16.
X.
Zhang
,
Integrability of Dynamical Systems: Algebra and Analysis
(
Springer
,
Singapore
,
2017
).
17.
A. V.
Tykhyy
,
Y. I.
Kolesnichenko
,
Y. V.
Yakovenko
,
A.
Weller
, and
A.
Werner
,
Plasma Phys. Controlled Fusion
49
,
703
(
2007
).
18.
A. V.
Tykhyy
and
Y. I.
Kolesnichenko
,
Plasma Phys. Controlled Fusion
63
,
075019
(
2021
).
19.
Y.
Kolesnichenko
,
V. V.
Lutsenko
,
A. V.
Tykhyy
,
A.
Weller
,
A.
Werner
,
H.
Wobig
, and
J.
Geiger
,
Phys. Plasmas
13
,
072504
(
2006
).
20.
S.
Gori
,
W.
Lotz
, and
J.
Nuhrenberg
, “
Quasi-isodynamic stellarators
,” in
Theory of Fusion Plasmas (Proceedings of Joint Varenna-Lausanne International Workshop)
(
Editrice Compositori
,
Bologna
,
1994
), p.
335
.
21.
C. D.
Beidler
and
H.
Maasberg
,
Plasma Phys. Controlled Fusion
43
,
1131
(
2001
).
22.
P.
Helander
and
J.
Nührenberg
,
Plasma Phys. Controlled Fusion
51
,
055004
(
2009
).
23.
P.
Helander
,
J.
Geiger
, and
H.
Maaßberg
,
Phys. Plasmas
18
,
092505
(
2011
).
24.
F.
Warmer
,
C. D.
Beidler
,
A.
Dinklage
, and
R.
Wolf
,
Plasma Phys. Controlled Fusion
58
,
074006
(
2016
).
25.
Y.
Kolesnichenko
,
V. V.
Lutsenko
, and
A. V.
Tykhyy
, “
Stochastic diffusion of fast ions in Wendelstein-type stellarators: Numerical experiment and extension of theory
,” in
17th IAEA TM on Energetic Particles and Theory of Plasma Instabilities in Magnetic Confinement Fusion
,
2021
.
26.
R.
Goldston
,
R.
White
, and
A.
Boozer
,
Phys. Rev. Lett.
47
,
647
(
1981
).
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