An exact analytic solution of the Vlasov equation for the plasma distribution in a Paul trap is known to be a Maxwellian and thus, immune to collisions under the assumption of infinitely fast relaxation [K. Shah and H. S. Ramachandran, Phys. Plasmas 15, 062303 (2008)]. In this paper, it is shown that even for a more realistic situation of finite time relaxation, solutions of the Fokker–Planck equation lead to an equilibrium solution of the form of a Maxwellian with oscillatory temperature. This shows that the rf heating observed in Paul traps cannot be caused due to collisional effects alone.
REFERENCES
1.
W.
Paul
, Rev. Mod. Phys.
62
, 531
(1990
).2.
R. C.
Davidson
, H.
Quin
, and G.
Shvets
, Phys. Plasmas
7
, 1020
(2000
).3.
K.
Shah
and H. S.
Ramachandran
, Phys. Plasmas
15
, 062303
(2008
).4.
K.
Shah
and H. S.
Ramachandran
, Phys. Plasmas
16
, 062307
(2009
).5.
K.
Avinash
, A. K.
Agarwal
, M. R.
Jana
, A.
Sen
, and P. K.
Kaw
, Phys. Plasmas
2
, 3569
(1995
).6.
M.
Sudakov
, Int. J. Mass. Spectrom.
206
, 27
(2001
).7.
A. A.
Makarov
, Anal. Chem.
68
, 4257
(1996
).8.
H.
Schaaf
, U.
Schmeling
, and G.
Werth
, Appl. Phys. (Berlin)
25
, 249
(1981
).9.
M.
Schubert
, I.
Siemers
, and R.
Blatt
, Appl. Phys. B: Lasers Opt.
51
, 414
(1990
).10.
R.
Iffländer
and G.
Werth
, Metrologia
13
, 167
(1977
).11.
R.
Blümel
, C.
Kappler
, W.
Quint
, and H.
Walther
, Phys. Rev. A
40
, 808
(1989
).12.
E. P.
Gilson
, R. C.
Davidson
, P. C.
Efthimion
, R.
Majeski
, and H.
Quin
, Laser Part. Beams
21
, 549
(2003
).13.
D. J.
Berkeland
, Rev. Sci. Instrum.
73
, 2856
(2002
).14.
D. J.
Wineland
, W. M.
Itano
, and R. S.
Van Dyck
, Jr., Adv. At. Mol. Phys.
19
, 135
(1983
).15.
J. F. J.
Todd
, Mass Spectrom. Rev.
10
, 3
(1991
).16.
S.
Sevugarajan
and A. G.
Menon
, Int. J. Mass. Spectrom.
218
, 181
(2002
).17.
D.
Zajfman
, Y.
Rudich
, I.
Sagi
, D.
Strasser
, D. W.
Savin
, S.
Goldberg
, M.
Rappaport
, and O.
Heber
, Int. J. Mass. Spectrom.
229
, 55
(2003
).18.
A.
Steane
, Appl. Phys. B: Lasers Opt.
64
, 623
(1997
).19.
D.
Kielpinski
, C.
Monroe
, and D. J.
Wineland
, Nature (London)
417
, 709
(2002
).20.
H. C.
Nägerl
, D.
Leibfried
, H.
Rohde
, G.
Thalhammer
, J.
Eschner
, F.
Schmidt-Kaler
, and R.
Blatt
, Phys. Rev. A
60
, 145
(1999
).21.
J.
Walz
, S. B.
Ross
, C.
Zimmermann
, L.
Ricci
, M.
Prevedelli
, and T. W.
Hansch
, Hyperfine Interact.
100
, 133
(1996
).22.
G. -Z.
Li
, R.
Poggiani
, G.
Testera
, G.
Torelli
, and G.
Werth
, Hyperfine Interact.
76
, 343
(1993
).23.
J. M.
Finn
, R.
Nebel
, A.
Glasser
, and H. R.
Lewis
, Phys. Plasmas
4
, 1238
(1997
).24.
S.
Chandrasekhar
, Rev. Mod. Phys.
15
, 1
(1943
).25.
I.
Siemers
, R.
Blatt
, Th.
Sauter
, and W.
Neuhauser
, Phys. Rev. A
38
, 5121
(1988
).26.
D. H. E.
Dubin
and T. M.
O’Neil
, Rev. Mod. Phys.
71
, 87
(1999
).27.
R. A.
Nebel
and J. M.
Finn
, Phys. Plasmas
7
, 839
(2000
).28.
D. C.
Barnes
and R. A.
Nebel
, Phys. Plasmas
5
, 2498
(1998
).29.
30.
M. N.
Rosenbluth
, W. M.
MacDonald
, and D. L.
Judd
, Phys. Rev.
107
, 1
(1957
).31.
K.
Shah
, Ph.D. thesis, Indian Institute of Technology Madras
, India, 2010
.32.
G. J.
Morales
and Y. C.
Lee
, Phys. Rev. Lett.
33
, 1534
(1974
).© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.
