Presented in the 12th International Workshop on ECRIS, RIKEN, Japan, 1995
STATUS OF ECRIS BUILDING AND RECENT RESULTS ON TRAP MODELLING
S. Biri, A. Valek and J. Vámosi
Institute of Nuclear Research (ATOMKI), Debrecen, HUNGARY
Abstract
In the ATOMKI a room-temperature, 14.5 GHz, one-stage ECR ion source has been designed and is being
built. The first plasma is expected by the end of 1995. The main design parameters and the present state of the low
energy accelerator (based on the ECR ion source) are shown.
Some new features have been included into the TrapCAD code. One-particle simulations of motion of
electrons and ions in the ECRIS trap are shown. Electron heating by crossing the resonance surface (assuming single
cavity mode) and multiple small-angle ion-ion scatterings are included.
Introduction
The Debrecen ECRIS project1 started in 1993.
A new group was organized in order to design, build,
start-up, operate and (with others) use an ECR type
highly charged heavy ion source.
The designing of the magnetic and mechanical
systems of the source have been finished in 1994. In
spite of the limited man-power and financial resources
the main parts of the ion source have been bought
and/or are being manufactured in the workshop of the
institute. The assembling of the ECR source is in
progress.
Until having a working ECR ion source the
secondary activity of the group is to study theoretically
the physics of the processes in the ECRIS chamber.
This is carrying out mainly by step-by-step developing
and using our special computer code, named TrapCAD.
This paper in the first section summarizes the
present status of the Debrecen ECRIS project. The
second section gives a short review on the TrapCAD
code and on the latest developments of the code. The
third section shows the usage of TrapCAD to simulate
the electron heating by ECR.
The ECR ion source:
(1) will serve as a source of low energy (up to
30*Q keV) ions for ion-atom and ion-surface collisions;
(2) serves and will serve as the subject of
theoretical and experimental research in order to study
the elementary processes in the ECR plasma chamber
and also for future developments of the ECRIS.
1.2 Mechanical design
The mechanical design follows the solutions of
the Frankfurt ECRIS [1]. The mechanical assembly has
the feature that the two big mirror coils are axially
movable together with theirs iron yokes. This way the
assembling and disassembling of the source can be
quick and easy and one also can change the positions of
the minimum and maximum of the axial magnetic field.
1.3 Magnetic system
In Fig.1 the magnetic arrangement of the ion
source can be seen.
a
12000
1. Status of the Debrecen ECRIS program
10000
1.1 Changing of the goal
Originally the ECR ion source was planned to
simultaneously serve as (1) injector into the K20
cyclotron of the ATOMKI, (2) injector into an 500 KV
electrostatic accelerator (to be built) and (3) direct
source of highly charged ions with an energy
determined by the potential of the plasma chamber.
For financial and other reasons the first part
(ECR+cyclotron) was cancelled, while the second one
was postponed.
a
8000
a
B
6000
Becr
4000
2000
0
a
1The Debrecen ECRIS program is supported by the National
Scientific Research Foundation (OTKA) under the contracts
No. A077, F013961, F015088 and by the FEFA under the
contract No. FEFA-697/2-AA-1.
Fig.1. The magnetic system of the ion source and the
calculated axial magnetic field distribution. 1,2 - iron,
3 - coils, 4 - NdFeB hexapole.
2
The inner diameter of the pancakes is 16.5 cm,
the outer is 48 cm. A relatively thick iron shielding (5
cm) is applied. The pancakes will be connected into
three groups (5, 2+2 and 5 pancakes, see the figure) and
supplied by a 3-channel 55 V/500 A power supply.
For the radial confinement the traditional
closed hexapole configuration was chosen. 24 Halbach
segments are glued together using NEOREM400i
(Br=1.30 T, jHc=1000 kA/m) and NEOREM490i
(Br=1.15 T, jHc=1900 kA/m) NdFeB materials. The
inner diameter of the hexapole is 6.5 cm, the outer is
13.5 cm, length is 20 cm.
Fig.2 shows the axial distribution of the
azimuthal and axial magnetic field components of the
hexapole at some radii. The radical changing of the field
components near the edge of the hexapole shows good
agreement with the semi-empirical formulas that were
described in our another paper [2] in details.
The radial component of the magnetic field can
be described by a T tapering function:
B r ( r, ϕ, z ) = B rp ( r, ϕ ) ⋅T ( r, z )
(1)
9000
a.)
8000
r=28 mm
7000
6000
5000
r=21 mm
4000
3000
2000
r=14 mm
1000
0
-50
0
50
100
150
200
250
z(mm)
3000
b.)
r=28 mm
2000
r=21 mm
1000
0
-50
0
-1000
50
100
150
200
250
r=14 mm
-2000
-3000
where B rp is the PANDIRA computed field and the
tapering function is the following:
L
M
Nd
i
T ( r, z ) = 0. 5 z z 2 + p2 ( r )
−1/ 2
O
P
Q
+1
(2)
The fitting p parameter was determined using some
experimental data [2]. The longitudinal z component of
the fringe field was calculated numerically according to
the rot B = 0 Maxwell equation.
Extrapolating from the figure the average total
magnetic field at r=29 mm (this is the inner radius of
the plasma chamber) is 0.95 T, while at r=32.5 mm (at
the magnet inner wall) is 1.2 T.
1.4 HF system
The new 14.5 GHz Varian GEN-III amplifier
was tested at 2 kW RF output power with good results.
A circulator with built-in loads was recently bought.
The building of the waveguide line between the
amplifier and the ion source is in progress.
1.5 Other parts
An independent water cooling system must be
built to eliminate the electrical power. The elements of
this cooling system has been recently ordered (dp=5
bar, Q=1 liter/s, Tin=60 C, Tout=25 C). The calculation
of the extraction optics is being carried out using the
IGUN code [3]. The 90 degree beam analyzing magnet
with 25 cm radius (Bmax=0.32 Tesla) has been ordered.
To control the beam selection GPIB card will be
applied. The laboratory originally used by the oldest
accelerator of the institute was completely renewed for
the ECR source.
z(mm)
Fig.2. Axial distribution of the azimuthal and axial Bcomponents of the hexapole at 3 radii. Symbols:
measured values (for a better visualization only every
fifth point is drawn). Continuous line: calculated curves
based on the equations (1)-(2).
2. The TrapCAD code
2.1 Features
The original goal to develop such a code was
to visualize the structure of the combined magnetic field
in the ECR chamber. Since then further ideas and
requirements were born and numerous other kind of
improvements have been carried out. Now the code is
applicable - with some restrictions - to simulate certain
elementary processes in the ECR magnetic trap.
The main functionalities presently built in the
code are:
• drawing field lines (one line or a set of lines);
• calculation several kind of mirror ratios of the field
lines;
• drawing flux tubes;
• drawing resonant zone and calculating its parameters;
• simulating the motion of electrons, optionally with
ECR heating;
• simulating the motion of ions, optionally including
ion-ion scatterings [4];
• possible switching on or off the edge effects of the
multipole;
• a constant electrostatic field can be applied;
3
• making 2D magnetic map file of a cross section of the
chamber at a specified degree;
• preparing DXF type files of all above for real 3D
visualization by AutoCAD.
In Fig.3 the typical graphical output of
TrapCAD can be seen with some explanation texts.
in the x-y plane of the chamber. The amplitude of this
field is calculated from the applied microwave power
assuming a value of 2.5 for the quality factor of the
loaded cavity. The initial phase difference between the
rotating electric field and velocity vector of the particle
can be specified by the user. Fig. 4 shows the energy
changings of the electron during multiple crossing the
resonant surface. The four curves represent four
different starting phases. One can see that the shape of
the energy function near the crossings is quite similar to
that can be deduced analytically [5] (where, however,
strong simplifications for the magnetic field were
assumed). It has to be also noticed that the time between
the passes becomes shorter if the particle energy is
increasing.
4000
3500
3000
2500
2000
Fig.3. Example output of TrapCAD. The figure
represents a 14.5 GHz plasma chamber with 1 Tesla Bfields at the walls.
1500
1000
500
0
0
2.2 Recent developments
Ion-ion scatterings. Considering the collision
(ion-ion, electron-electron, electron-ion) and charge
exchange (ionization, ion-ion charge exchange)
processes in the plasma, one can find that the rate of the
ion-ion collision is much higher than the rates of the
other processes [4].
As a result, the valid simulation time without
interactions for electrons is under 1 ms, for ions is under
1 µs. If the user wants to simulate a motion of an ion for
a longer period than 1 µs the ion-ion collisions must be
included in the calculation. The feature of the ion-ion
collision was built into the TrapCAD code. For
simplicity, the multiple small-angle scatterings were
replaced by Boltzmann distributed large-angle single
collisions.
Added electrostatic field. To simulate the
effect of constant external fields (e.g. extraction field,
biased disc) inside the plasma chamber, a homogeneous
electrostatic field can be defined. This field has two
component: the axial component in the z-direction and
the component in the x-y plane.
Electron heating. The exact, mathematical
description of the electron heating by electron cyclotron
resonance is quite complicated because of the many
high frequency modes inside the chamber. However, the
stochastic process can be studied and one can get valid
values for the energy gaining assuming a much simpler
RF field but using a realistic magnetic field
configuration. In the TrapCAD a circularly polarized
plane wave is assumed that is propagating along the z
axis. The electric vector of this type of wave is rotating
50
100
150
200
t (ns)
Fig.4. Example of the ECR heating of the electrons
simulated by TrapCAD. Four electrons having the same
initial energy (100 eV) started with different phases.
UNIX version. When simulating an electron motion for
a time period in the range of 1 µs the actual CPU time
on a PC 486 can be some hours. To reduce the time of
calculation the source code of TrapCAD was adapted to
UNIX workstations (using the large scale portability of
the C language). The graphics routines of the code were
omitted. The input data are taken from input files and
the results of the simulation (the path and the energy of
a heated particle) are redirected also output files. This
way the simulation time can be reduced (e.g. on a
Silicon Graphics Indy) by one order.
3. Electron heating
3.1 The goal of the simulation
The goal of the simulation described in this
section was to answer the question: what happens to the
energy of a set of single electrons after multiple
crossing the resonant surface?
We have to neglect collective effects, that is
why the simulation time must be well within the
average collision and ionization times of the electrons
(see 2.2). On the other hand, the phase between the field
strength and the perpendicular velocity vectors is not
random or stationary as it is usually assumed, but -
4
3.3 Results - average energies
Fig.5 shows the evolution of the average
electron energy applying different HF powers. The
curves are near linear within the simulation time.
However, the slopes of the curves increase less than the
HF power. It is also clear that the average energy is not
depend on the initial energy of the electrons.
Some of the electrons were lost within the
simulation time, because they got into the magnetic loss
7000
6000
5000
P_rf=1000 W
P_hf=500 W
4000
3000
2000
P_hf=100 W
1000
0
0
200
400
600
800
1000
t (ns)
Fig.5. Evolution of the average energy of 180 electrons
applying different HF powers. The initial electron
energy was 100 eV.
3.4 Results - energy distributions
Examining the electron energies in different
moments the electron distributions can be obtained and
compared. Although the total number (180) of the
electrons seems to be too few for this purpose, the result
is quite promising. The hystograms in Fig.6 clearly
show the appearance and evolution of the high energy
tail of the energy function.
140
electron number
120
100
80
60
40
20
700
0
0.85
2.55
4.25
5.95
7.65
9.35
11.1
12.8
14.5
16.2
3.2 Input data
Electron number and starting positions. The
motion of 180 independent, single electrons was
examined. The 180 electrons were divided into 5 groups
with 36 electrons in each. These groups started from
different positions of the chamber (2 points at the
'middle circle' of the zone and 3 points near the 'edge' of
the resonant zone), where the magnetic field strength
was just below the resonant value (that is all the
electrons started from inside the resonant zone). All the
electrons had the same initial energy, however, the
phase between theirs velocity and the electrical field
was varied by 10 degrees in each group from zero to
350. The above 'run' was repeated several times
changing the initial energy, or the HF-power (see
below).
Geometry. The dimensions of the Debrecen
ECRIS were used: d=6 cm, l=20 cm.
Frequency: 14.5 GHz.
Axial magnetic field. A symmetrical field was
used with 1 T peaks at the ends of the chamber.
Radial magnetic field. 1 T hexapole field at
the chamber wall.
Starting energy. The total initial energy for
each electrons was chosen to be equal for simplicity
(100 or 1000 eV). The initial perpendicular/parallel
ratio was always 100.
HF power. 3 cases were examined with HF
power of 100, 500 and 1000 W.
Simulation time. In [4] (and in shortly in 2.2)
a rough estimation was given for the mean collision
time of the electrons. It was found to be about 100
microsecond for one single electron. To eliminate the
possibility of the collective effects, the simulation time
here was chosen to be 2 order less that is 1
microsecond.
The calculations were run on UNIX
workstations. The estimated total CPU time was 25
hours.
cone and hit the wall. That is the reason that each curves
are represented in double. The upper ones mean a real
average, that is the total energy of the existing electrons
are divided by the number of the existing electrons. For
the lower curves the total energy is divided by always
180 (the initial electron number). This way the lower
curves show the tendency of the electron losses.
E (eV)
starting from some initial values - is calculated in each
step and at the moment of energy gaining or loosing it
can be considered as some kind of 'real stochastic'
value.
The initial position, energy, and phase of the
electrons must be chosen such a way that the electrons
can cross the resonance surface many times during the
simulation time.
300
50
t (ns)
E (keV)
Fig.6. Typical electron energy distributions obtained by
simulating the heating of 180 electrons. The initial
energy was 1 keV, incident HF power 500 W.
Similarly, in Fig.7a the energy distribution is shown at
3 different moments. Fig.7b shows the effect of the HF
power on the energy distribution. Exponential curves
were used for fitting.
5
Conclusion
180
a.)
160
140
E_start=100 eV, P_hf=1000 W
50 ns
120
400 ns
n
References
1000 ns
100
[1] K.E.Stiebing et al, see this proceedings.
[2] J.Vámosi, S.Biri, Nucl.Instr.Methods, B94 (1994)
297-305.
[3] R.Becker and W.B.Herrmannsfeldt, Rev.Sci. Instr.
Vol.63, No.4., Part II (1992) pp. 2756-2758.
[4] S. Biri, J. Vámosi, K.E. Stiebing, H. ScmidtBöcking, 7th Int. Conf. Phys. High. Charg. Ions
(HCI94), 1994, Vienna (Proc. will be published in Nucl.
Instr. Methods).
[5] Y.Jongen, Proc. 6. Int. Workshop on ECRIS, LBL,
1985, pp.238-255.
80
60
40
20
0
0
10000
E (eV)
20000
30000
150
b.)
125
E_start=100 eV, t=300 ns
P=100 W
100
P=500 W
P=1000 W
n
The building of the Debrecen ECR ion source
is in progress. The first plasma is expected in 1995,
while the first beam is planned in 1995/96.
The electron heating calculation proved that
numerous experimental results can be qualitatively well
simulated. Using more realistic HF modes the results
can be even more closer to the real phenomena.
75
50
25
0
0
5000
E (eV)
10000
15000
Fig.7. Evolution of the electron energy distribution (a).
Effect of the HF power on the energy distribution (b).