beam is turned off. Therefore, this should be considered in the experimental sequence of producing and ejecting the highly charged ions from the EBIS. It is also necessary to predict the total amount of charge that can stably trap in this breeding region. The trap capacity can be calculated using Eq. (2.31) [56],
CTrap=1.05×1013 IeL
√Ee
f, (2.31)
whereIe, L, Ee, and f are the electron beam current, the length of the breeding region, the energy of electrons, and the charge compensation, respectively. The length of the RAON EBIS breeding region is 0.76 m, and when an electron beam 1 A is transmitted with an energy of 13 keV, the trap capacity becomes∼7.00×1010charges when the charge compensation is 1. That is, based on132Sn25+, about 2.8×109 particles can be trapped. However, the number of trappable particles is reduced when there is a charge compensation effect, including the capacity loss caused by the residual gas inside the EBIS.
Considering the bunch capacity, which is one of the specifications of RFQ-CB that sends the bunched ion beam to the EBIS, it seems that the trap capacity could sufficiently trap it.
𝑥𝑥 𝑥𝑥′
𝜀𝜀 𝛾𝛾 𝜀𝜀
𝛽𝛽
𝛽𝛽𝜀𝜀 𝛾𝛾𝜀𝜀
tan2𝜙𝜙= 2𝛼𝛼 𝛾𝛾 − 𝛽𝛽
𝜙𝜙
Figure 2.13: Phase-space ellipse with relations for extrema, and intercepts described by emittance and Twiss parameters.
The maximum emittance of the beam that can be injected into the EBIS and overlap with the elec- tron beam is expressed as acceptance, which becomes the beam injection condition of the EBIS. To
- 4 0 - 2 0 0 2 0 4 0
- 4 0 - 2 0
0
2 0 4 0
I n p u t 1 0 0 %
x' [mrad]
x [ m m ]
(a) Input and 100% overlap.
- 4 0 - 2 0 0 2 0 4 0
- 4 0 - 2 0
0
2 0 4 0
I n p u t 2 0 ~ 4 0 % 4 0 ~ 6 0 % 6 0 ~ 8 0 % 8 0 ~ 1 0 0 % 1 0 0 %
x' [mrad]
x [ m m ]
(b) Input and each overlap fraction.
Figure 2.14: Initial simulation using 2511 samples of EBIS acceptance by TRAK.
calculate this acceptance, a beam distribution was created on the phase-space, as shown in the gray dots in Fig. 2.14a, and the ratio of overlapping the electron beam in the breeding region was simulated by TRAK. 2511 samples of133Cs1+with 20 keV energy were injected on the potential distribution with the electron beams transmitted in Figs. 2.11 and 2.12. The initial position of the generated beam distribution
was set to the position where the pepperpot emittance meter before the repeller, introduced in Sec. 3.3.1, can measure the emittance of the beam entering the EBIS in the experiment. In Fig. 2.14b, compared to the electron beam size of 0.437 mm, within the breeding region, in the range ofz= 1.2 to 1.5 m in simulation. From the result, the overlapping ratio with the electron beam was expressed in 20% steps, and the condition for overlapping more than 20% is 40.5π·mm·mrad. The red color in Fig 2.14a was particles that 100% overlap the electron beam, and the acceptance was 1.68π·mm·mrad.
In Fig. 2.14b, an area overlapped with the electron beam by more than 20% was confirmed in the phase-space, and this area was further divided, and the number of samples increased to 10521. In addition, the upper right and lower left regions, which have no effect on accpetance, were completely excluded. So, the initial beam distribution as the gray dot in Fig. 2.15a was created as a parallelogram region, including the diagonal ellipse region. Using this input beam, the acceptance was more accurately calculated with TRAK, as shown in Fig. 2.15, expressed at 20% intervals, as in Fig. 2.14. A clearer form
- 4 0 - 2 0 0 2 0 4 0
- 4 0 - 2 0
0
2 0 4 0
I n p u t 1 0 0 %
x' [mrad]
x [ m m ]
(a) Input and 100% overlap.
- 4 0 - 2 0 0 2 0 4 0
- 4 0 - 2 0
0
2 0
4 0 I n p u t
2 0 ~ 4 0 % 4 0 ~ 6 0 % 6 0 ~ 8 0 % 8 0 ~ 1 0 0 % 1 0 0 %
x' [mrad]
x [ m m ]
(b) Input and each overlap fraction.
Figure 2.15: Simulation using 10521 samples of EBIS acceptance by TRAK.
of the acceptance area on the phase space could be confirmed. The 20% or more and 100% accpetance values were 30.8π·mm·mrad and 7.30π·mm·mrad, respectively, and this ellipse also shows the conditions under which the beam should be focused and transmitted. In the ion beam experiments, the emittance of the beam entering the EBIS is measured, and it is transmitted having smaller than 100%
acceptance,εAccept. And it is focused using the beam optics so that the electron beam and ion beam can be completely overlapped.
When the ions under the 100% acceptance condition reached a charge state of 33+ (A/q = 4.03) in the trap region, they were extracted with an energy of 10 keV/u by setting the platform voltage to 40 kV. Each ion’s position and transverse velocity were fixed in the breeding region, and the direction of the longitudinal velocity was changed. In addition, the charge state of all ions was substituted from 1+
to 33+, and the potential distribution of the drift tube in the breeding region was changed to about 40 kV.
Figure 2.16 shows the results of the transmission simulation of133Cs33+set in this way up to the initial
- 1 5 - 1 0 - 5 0 5 1 0 1 5 - 6
- 4 - 2
0246
εx = 1 . 3 5 π∙m m ∙m r a d
x' [mrad]
x [ m m ]
(a) Horizontal phase-space.
- 1 5 - 1 0 - 5 0 5 1 0 1 5
- 6 - 4 - 2
0246
εy = 1 . 5 3 π∙m m ∙m r a d
y' [mrad]
y [ m m ]
(b) Vertical phase-space.
Figure 2.16: Phase-space of ejected133Cs33+ions with 10 keV/u simulated by TRAK.
position of the acceptance simulation. As a result of this simulation, first of all, the ellipse in the phase- space is tilted in the defocusing direction, and the horizontal and vertical emittance values are 1.35 and 1.53, respectively. The transverse emittances are about one-fifth of the acceptance value, but it comes from the energy difference of the beam. When the ion beam is injected, the energy is 20 keV, and when it is extracted, the energy is 1330 keV, which increases about 66 times, which means that the longitudinal speed increases about 8 times. Since the value ofx′is inversely proportional to the energy for the same transverse velocity, as the longitudinal velocity increases eight times, the value ofx′ decreases eight times. Considering the reducedx′ by the energy difference, it shows a slight increase compared to the previous one. But it shows a sufficiently low emittance, which shows that the transmission of the highly charged ions can be stably performed.
During the charge breeding, ions trapped in the EBIS have an energy distribution due to collisions with each other. The energy of the ion beam is formed as a Boltzmann distribution like Eq. (2.35) in about ms [56]. This energy distribution characteristic gives rise to the loss term due to the ion heating in Sec. 2.1 for the charge breeding effect.
f(E) = 2
√πkBT r E
kBTexp E
kBT
. (2.35)
However, before the loss occurs, it is possible to predict the energy characteristics of the ion beam in the EBIS. Since highly charged ions have the energy of the Boltzmann distribution with the exponential term, the voltage waveform can be determined for the pulse stretching introduced in Sec. 4.3.4. When a beam is extracted by applying a voltage to the drift tube in the form of a logarithmic function, which is an inverse function of the Boltzmann distribution, a long flat top-shaped ion beam pulse can be created through the pulse stretching.
Chapter 3
Experimental Setup
This chapter contains a detailed experimental setup of the RAON EBIS charge breeder. The basic design and fabrication of RAON EBIS have already been done [16–18, 47, 58], and there have been some mod- ifications, complements, and sub-system changes since then. It briefly describes the previous design’s essential parts and the changes and sub-systems prepared for the experiment. As shown in Fig. 1.4, the structure of the RAON EBIS charge breeder can be divided mainly into the electron gun section, the ion trap section, the collector and the repeller section, and the ion transportation line. Figure 3.1 shows the schematic drawing of the overall system of the EBIS, including the electrode arrangement for each section along the path of the ion beam from and to the ISOL beamline. Each electrode’s color represents each HV platform and is the EBIS, the cathode, the repeller, the ion source, and the ground platform, respectively. The electron gun, the collector, and the repeller are important for the electron beam uti- lization, starting with the ion trap section where the charge breeding of the ion beam takes place. Their detailed setup is described for each section divided in this way. After that, the installation and utilization of the ion transportation line, which is essential for connecting with the ISOL beamline and the beam diagnosis, are described. Finally, the detailed setup of subsystems, including the vacuum systems, which are important for the charge breeding experiment of the EBIS, is shown.