[i] mastersthesis
DESCRIPTION
[I] MastersThesisTRANSCRIPT
-
RICE UNIVERSITY
NOVEL PERMANENT-MAGNET PENNING TRAP
FOR STUDIES OF DIPOLE-BOUND NEGATIVE IONS
by
Leonard Suess
MASTER OF SCIENCE
HOUSTON, TEXAS
DECEMBER, 2001
-
RICE UNIVERSITY
Novel Permanent-Magnet Penning Trap
for Studies of Dipole-Bound Negative Ions
by
Leonard Suess
A THESIS SUBMITTED
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE
Master of Science
APPROVED, THESIS COMMITTEE:
F.B. Dunning, ChairProfessor of Physics
G.K. Walters, Sam and Helen WordenProfessor of Physics, Emeritus
P. PadleyAssistant Professor of Physics
HOUSTON, TEXAS
DECEMBER, 2001
-
ABSTRACT
Novel Permanent-Magnet Penning Trap
for Studies of Dipole-Bound Negative Ions
by
Leonard Suess
Low-energy electron transfer between a Rydberg atom and a target molecule can
result in formation of long-lived metastable negative ions. Here we describe a novel permanent-
magnet Penning trap designed to examine the lifetime of such long lived metastable negative
ions. With the help of ion trajectory calculations, the characteristics of the trap have
been investigated and the most eective methods for ion injection have been established.
Collisions with SF6, which has a high electron attachment rate, result in the formation
of SF6 ions which are known to have a long intermediate lifetime. Comparisons between
experimental SF6 trapping data and ion trajectory calculations are discussed that demonstrate
the capabilities of the trap. Future experimental studies are also proposed.
-
Acknowledgments
A big thank you to Dr. Barry Dunning for his guidance and insight. Priya, thanks
for sharing your knowledge with me and for being such a wonderful friend. I am grateful to
Shannon Hill whose tireless eorts allowed a detailed investigation of the trap used in this
work. I have also beneted greatly from the interactions of all the other graduate students
and post docs in the laboratory. Their advice and contributions are greatly appreciated.
I would like to thank my family for their love and support. I am grateful to my
parents, who have constantly pushed me to better myself.
Most importantly, my deepest thanks go to my wife, Jessica. Her constant support
and love continues to push me forward.
-
Table of Contents
Abstract iii
Acknowledgments iv
List of Figures vii
1 Introduction 11.1 Electron Attachment Processes . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Rydberg Atom Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Ion Kinematics in an Ideal Penning Trap 42.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Equations of Motion for an Ion in an Ideal Penning Trap . . . . . . . . . . 5
2.2.1 Radial Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Axial Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Trapping Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Cylindrical vs. Ideal Penning Trap . . . . . . . . . . . . . . . . . . . . . . . 8
3 Experimental Apparatus 113.1 Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Potassium Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Permanent-Magnet Cylindrical Penning Trap . . . . . . . . . . . . . . . . . 16
3.4.1 Cladding Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.2 Trap Electrode and Electronics . . . . . . . . . . . . . . . . . . . . . 24
4 Simulating Ion Trajectories SIMION 284.1 Experimental Model in SIMION . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Loop Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Electric Potential Distributions for Trap Electrodes . . . . . . . . . . . . . . 304.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Experimental and Analytical Techniques 335.1 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 SF6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6 Conclusion and Future Work 406.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
v
-
References 42
A SIMION Code for Simulations 44
B Important Trap Dimensions and Characteristics 48B.1 Trap Dimensions and Quantities . . . . . . . . . . . . . . . . . . . . . . . . 48
vi
-
List of Figures
2.1 Ideal Penning trap with hyperbolic electrodes. . . . . . . . . . . . . . . . . 4
2.2 Magnetron motion superimposed on the cyclotron motion. . . . . . . . . . 5
2.3 Graph of expansion coecients D2 and D4 as functions of r0z0 . . . . . . . . 10
3.1 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Comparison of dierent magnetic materials. . . . . . . . . . . . . . . . . . 17
3.3 Magnetic Ohms analog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Cladding magnet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Cross-sectional view of clad magnet. . . . . . . . . . . . . . . . . . . . . . . 21
3.6 Comparison of unclad and clad magnetic structures. . . . . . . . . . . . . . 22
3.7 Magnetization of the magnet assembly. . . . . . . . . . . . . . . . . . . . . 23
3.8 Axial magnetic eld within the magnet. . . . . . . . . . . . . . . . . . . . . 25
3.9 Cross-section of trap electrode. . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.10 Schematic of switching circuit. . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1 SIMION model of experimental setup. . . . . . . . . . . . . . . . . . . . . . 28
4.2 Potentials on trap electrodes for various modes . . . . . . . . . . . . . . . . 31
4.3 Extraction of axial frequency for SF6 . . . . . . . . . . . . . . . . . . . . . 32
5.1 Pulse sequence for the bottom grid of the interaction region. . . . . . . . . . 34
5.2 TOF for 300s trapped SF6 ions. . . . . . . . . . . . . . . . . . . . . . . . 36
5.3 Arrival time spectrum for trapping times 185,300, and 416s. . . . . . . . . 37
5.4 Arrival time spectrum for a trapping time of 358s. . . . . . . . . . . . . . 38
5.5 Stability of SF6 in Penning trap. . . . . . . . . . . . . . . . . . . . . . . . 39
A.1 Electrode numbers for SIMION . . . . . . . . . . . . . . . . . . . . . . . . . 47
vii
-
Chapter 1
Introduction
1.1 Electron Attachment Processes
The study of electron-molecule interactions has grown signicantly over the past sev-
eral years due to their importance in biological, chemical, and physical systems [1, 2]. For
example, electron attachment is important in atmospheric studies involving pollutants such
as polycyclic aromatic hydrocarbons and multiply halogenated methane and ethane com-
pounds. Studies of their interaction with free electrons provide rate constant data used for
modeling their behavior in the atmosphere [3, 4].
Electron attachment to molecules can lead to reactions of the form,
e +ABC ABC ABC + e, (1.1.1)
e +ABC ABC AB + C, (1.1.2)
e +ABC ABC ABC. (1.1.3)
In reaction 1.1.1, the transient negative ion formed reverts back into a neutral molecule and
an electron (autodetachment). In reaction 1.1.2, the intermediate dissociates producing
a neutral and a charged fragment. In reaction 1.1.3, the intermediate is stabilized by
intramolecular vibrational relaxation leading to formation of long-lived metastable negative
ions. For the present study, particular attention is paid to the formation of long-lived anions.
Here we study the properties of negative ions that are created through electron transfer
in collision with potassium atoms in high-lying Rydberg states. Rydberg atoms, atoms in
states of high principal quantum number n, exhibit exaggerated properties. Typically, the
1
-
2separation between the core ion and the excited electron is such that the target molecule
views the highly-excited atom as two independent scatters.
One of the major benets in utilizing Rydberg atom techniques for studying electron
attachment processes is the extremely low energy of the attaching electron. Its mean kinetic
energy, which is equal to its binding energy, can be varied from a few meV down to eV
by changing the principal number, n, of the atom. The velocity of the electron in its orbit
is high compared to the relative velocity of the atom and the target molecule at thermal
temperatures; thus, the energy (velocity) of the electron dominates the interaction.
1.2 Rydberg Atom Properties
The physical characteristics of Rydberg atoms are quite dierent from those of atoms
in ground or low-lying excited states. This is illustrated by Table 1.1 which lists a number
of atomic properties, their dependence on n, and representative values for each at several
n.
Property scaling(a.u.) n=1 n=15 n=30
Mean radius n2 5.3 109cm 18nm 48nm
Orbital period 2n3 1.5 1016s 0.5ps 4.5ps
Binding Energy 12n2
13.6eV 60meV 15.1meV
Radiative Lifetime 0n3 6.78ns 22.9s 183s
Table 1.1: Properties of Rydberg atoms.
The large size of the Rydberg atom indicates a large separation between the excited
electron and the core ion. For n 10, the separation between the core ion and the excited
-
3electron is greater than the range typical of either electron/molecule or ion/molecule in-
teractions; therefore, during collision with a neutral target, the Rydberg core and excited
electron act as independent scatters leading to the so-called essentially-free electron model.
-
Chapter 2
Ion Kinematics in an Ideal Penning Trap
2.1 Introduction
Figure 2.1: Ideal Penning trap with hyperbolic electrodes.
The conning of ions in a trap has been extensively studied since 1936 when Francis
Michel Penning applied an axial magnetic eld to an electric discharge to increase the path
length of electrons [5]. The basic structure of a Penning trap consists of three electrodes: two
end-cap electrodes and a ring electrode, as shown in Figure 2.1 immersed in a homogenous
axial magnetic eld. This axial eld causes ions to move in circular cyclotron orbits conning
them in the radial direction [6]. Axial connement is achieved by applying constant electric
potentials to the electrodes. The superposed E,B elds trap the ion, but introduce another
particle motion due to EB-terms called the magnetron motion. The magnetron motion
is superimposed on the cyclotron motion as seen in Figure 2.2 and ultimately determines
trap lifetime [5].
4
-
5Figure 2.2: Magnetron motion superimposed on the cyclotron motion.
2.2 Equations of Motion for an Ion in an Ideal Penning Trap
In an ideal hyperbolic Penning trap as shown in Figure 2.1 with endcaps separated by
a distance 2zo and a ring of radius r0, these parameters are related by, r0 =2z0.
For a charged particle in a constant electric eld and a magnetic eld orientated along
the z axis, the scalar potential , and the magnetic eld B are given by,
B = B0z, (2.2.1)
=V
2z2o + r20
(2z2 x2 y2) = 1, (2.2.2)
where V is the potential applied to the endcap electrodes with respect to the ring electrode,
B0 is the magnetic eld strength inside the trap and 1 is the electric potential inside the
trap generated by the endcaps.
The Lorentz force felt by a charged particle of mass m and charge q is,
F = q (E+ v B) , (2.2.3)
-
6taking the dot product with x, y and z respectively yields,
Fx = mx = q (1 x+ (v B) x) , (2.2.4)
Fy = my = q (1 y + (v B) y) , (2.2.5)
Fz = mz = q (1 z + (v B) z) . (2.2.6)
Using v = (x, y, z) and B = (0, 0, B0) yields,
x = cy +1220zx, (2.2.7)
y = cx+ 1220zy, (2.2.8)
z = 20zz, (2.2.9)
where 0z is the axial frequency,
0z =
4qV
m(r20 + 2z
20
) , (2.2.10)and c is the cyclotron frequency,
c =qB0m
. (2.2.11)
2.2.1 Radial Motion
To determine the radial motion of the ion in the Penning trap, solving the coupled
dierential equations 2.2.7 and 2.2.8 would be necessary as r = xi + yj. Introducing the
variable u dened by,
u x+ iy, (2.2.12)
allows for the decoupling of equations 2.2.7 and 2.2.8. Dierentiating this equation twice
yields,
u = icu+ 1220zu. (2.2.13)
-
7Using u = eit, the following characteristic equation is obtained,
22 2c + 20z = 0, (2.2.14)
the roots of which are,
=12
(c
2c 220z
). (2.2.15)
If 2c 220z < 0, then u will be characterized by an exponential decay and the ion will no
longer be trapped (i.e., loses its harmonic characteristic). Dening,
01 =2c 220z, (2.2.16)
we obtain two frequencies,
+ =12(c + 01) , (2.2.17)
=12(c 01) , (2.2.18)
where + is the modified cyclotron frequency and is the magnetron frequency. The
general solution of Eq. 2.2.13 is [5],
u = Aei+t +Beit, (2.2.19)
squaring and adding the x and y components of Eq. 2.2.19 gives,
x2 + y2 = |A|2 + |B|2 + 2|A||B| cos . (2.2.20)
Since 1 cos 1, this equation implies that the radial motion of the ion will oscillate
between an outer radius of |A+B| and an inner radius of |AB|.
2.2.2 Axial Motion
The axial motion of the ion can be extracted from Eq. 2.2.9 which represents the equa-
tion of a harmonic oscillator with natural frequency 0z. The particle will therefore oscillate
in the axial direction with frequency given by Eq. 2.2.10.
-
82.3 Trapping Requirements
From the above analysis, three independent and uncoupled degrees of motion are ap-
parent: cyclotron, magnetron and axial motions. Conditions for trapping an ion in an ideal
Penning trap are [5],
+ c 0z , (2.3.1)
Under realistic conditions, it is sucient that Eq. 2.2.15 be satised,
c >20z. (2.3.2)
What does Eq. 2.3.2 represent in terms of experimental parameters? Using the denitions
of c and 0z the answer is,
V trap->ejection)----
seg fast_adjust rcl inject_voltage ;;initializes electrodes:3,5,16,17 sto adj_elect16 rcl trapping_voltage sto adj_elect17 rcl inject_voltage sto adj_elect05 rcl trapping_voltage sto adj_elect03 ;;finishes the initialization
44
-
45
rcl switch_time rcl ion_time_of_flight xswitchtime, then trap
rcl switch_time rcl trapping_time add ;;total trap time is rcl ion_time_of_flight ;;switch_time+trapping_time x>y gosub eject ;;if tof> total trap time, then eject
exit ;;when cycle complete, exit
;;---thus ends the fast adjustment routine-----------------------------
;;---this is the inject subroutine that the program will call upon-------
lbl inject rcl inject_voltage ;;this subroutine recalls voltages sto adj_elect05 ;;defined by inject_voltage and rcl inject_voltage ;;trapping_voltage for ion's injection sto adj_elect16 ;;into trap. rcl trapping_voltage sto adj_elect03 rcl trapping_voltage sto adj_elect17 rtn ;;when all is done return to program
;;---this is the trap subroutine that is called upon by the program-----
lbl trap rcl ion_time_of_flight ;;this subroutine performs the trap rcl switch_time ;;ramp and stores it as volt_voltage subtract ;;which is later used in electrode#5 chs ;;-(tof-switchtime) rcl tau_time 1/x ;;1/(tau_time) multiply ;;-(tof-switchtime)/(tau_time) e^x ;;e^(-(tof-switchtime)/(tau_time)) chs ;;-e^(-(tof-switchtime)/(tau_time)) 1 add ;;1-e^(-(tof-switchtime)/(tau_time)) rcl inject_voltage rcl trapping_voltage subtract ;;(inject_voltage-trapping_voltage) multiply ;;(Vin-Vtr)(1-e^(-(tof- switchtime)/(tau_time))) chs ;;-(Vin-Vtr)(1-e^(-(tof-switchtime)/(tau_time))) rcl inject_voltage add ;;Vin-(Vin-Vtr)(1-e^(-(tof-switchtime)/(tau_time))) sto volt_voltage rcl volt_voltage
-
46
sto adj_elect05 ;;above voltage is stored in electrodes#: rcl volt_voltage ;;5,16 (which is the entrance to the trap). sto adj_elect16 rcl trapping_voltage ;;trapping_voltage is stored inelectrodes#: sto adj_elect03 ;;3, 17 (which is the exit to the trap). rcl trapping_voltage sto adj_elect17 rtn ;;when all is done, return to program
;;---this is the eject subroutine that the program so gladly uses-----
lbl eject rcl trapping_voltage ;;this subroutine switches the exit electrode sto adj_elect16 ;;of the trap from trap mode to ejection mode rcl trapping_voltage ;;electrodes#: 16, 5 stay in trap mode, but sto adj_elect05 ;;electrodes#: 17, 3 switch from trap to rcl ejection_voltage ;;ejection mode (i.e., trapping_voltage sto adj_elect17 ;;->ejection_voltage) rcl ejection_voltage sto adj_elect03 rtn ;;return to program when all is done
seg tstep_adjust ;;this routine adjusts the time step of the rcl ion_time_step 0.01 ;;calculations. x>y exit ;;if 0.01>ion_time_step then exit sto ion_time_step ;;else store the ion_time_step
lbl pe_update rcl update_flag x=0 rtn 0 sto update_flag 1 sto Update_PE_Surface rtn
-
47
20
1 23
45
6 7
8 9
10111213
1415
16171819
Figure A.1: Electrode numbers for SIMION code reference.
-
Appendix B
Important Trap Dimensions and Characteristics
B.1 Trap Dimensions and Quantities
z0 = 4cm (B.1.1)
r0 = 4.2cm (B.1.2)
B0 = .3T (B.1.3)
d20 = 12.4cm2 (B.1.4)
D2 = 1.1 (B.1.5)
D4 = 0.1 (B.1.6)
where z0 is one half the trap length, d20 =12
(z20 +
12r
20
),and D2 and D4 are expansion
coecients in Eq. 2.4.1.
V