In linear accelerators, beam is almost axisymmetric along the focusing periods but the anisotropy be- tween transverse and longitudinal directions can be easily happen. For anisotropic beams that have different RMS envelope size and emittance inxandzdirections along the linac, the emittance exchange between the two spaces can occur within the stop band indicated by Hofmann chart. As discussed in Sec. 3.3, the stop bands of the emittance exchange of anisotropic beams are simply represented by Hofmann chart as shown in Fig. 7.21. The colors in the Hofmann chart indicates the growth rates of exchange as a function of tune depression ratiosσx/σx0andσz/σx.
Figure 7.21 shows the Hofmann chart when the initial emittance ratio between x and z isεz/εx=3.
The stop bands are composed of the second-order, third-order, and fourth-order resonances. As shown in the Hofmann chart, the growth rates generated from emittance exchange increase as the anisotropy
Figure 7.21: Hofmann chart from TraceWin simulation code when the initial emittance ratio isεz/εx=3 as a function of tune depression ratiosσx/σx0 andσz/σx. The colors within the stop bands indicate the growth rates of emittance exchange. Black lines correspond toσx/σx0=0.5.
increases (i.e., εz/εx is far from the unit value 1) and the tune ratios are close to 1 (i.e., σz/σx ∼1).
The black lines in Fig. 7.21 correspond toσx/σx0=0.5, where the second and fourth-order instabilities affect the emittance exchange.
Figure 7.22: Emittance exchange between x and z directions when the initial beam parameters are εz/εx=3,σx/σx0=0.5, andσx0=80◦as a function of tune ratioσz/σx. Forσz/σx>2, large emittance growth occurs in longitudinal space because of the fourth-order particle resonance and envelope insta- bility (green box).
For Gaussian density beams, only non-oscillatory instability affects the emittance exchange and the stop bands of Hofmann chart applies to the space-charge driven coherent resonances of K-V beams.
Figure 7.22 shows the growth rates from emittance exchange betweenxandzdirections when the ini- tial beam parameters are εz/εx=3, σx/σx0=0.5, and σx0 =80◦ as a function of σz/σx. Here, the multiparticle simulations are done by TraceWin code with 3D bunched Gaussian beams.
Figure 7.22 (a) shows the emittance growth along 20 solenoid focusing periods. The maximum
emittance growth occurs whenσz/σx∼1.4. The space-charge effects shift the tune depression ratio in which the emittance exchange occurs from the unit value 1. Also, because the initial RMS emittance in transverse plane is smaller than that in longitudinal plane, the transverse emittance increases (black line) and longitudinal emittance decreases (red line). The emittance exchange effects are generated from the non-oscillatory instability and the phase space plots in x and z planes are shown in upper part of Fig. 7.22 (a). Forσz/σx>2, marked by green box, the 4σ=360◦ fourth-order particle resonance is manifested in the longitudinal space. In that reason, the red line in Fig. 7.22 (a) increases above the equilibrium line (∆εz/εz0=0).
Figure 7.22 (b) shows the emittance growth along 100 solenoid focusing periods. After 100 lattice periods, the emittance growth in longitudinal space for the region ofσz/σx>2 becomes large because of the excitation of the envelope instability which is excited following the fourth-order particle resonance.
In this case, the large emittance growth in one plane (red line) is related to the oscillatory instability in the anisotropic beams. In the upper plots of Fig. 7.22 (b) shows the four-fold structure at cell 20 and it grows to the envelope instability after long periods.
Figure 7.23: Emittance exchange between x and z directions when the initial beam parameters are εz/εx =3, σx/σx0=0.5, and σx0=100◦ as a function of tune ratio σz/σx. In this case, the fourth- order particle resonance and envelope instability can be manifested in both transverse and longitudinal spaces.
Figure 7.23 shows the growth rates from emittance exchange betweenxandzdirections when the initial beam parameters areεz/εx=3,σx/σx0=0.5, andσx0=100◦as a function ofσz/σx. In this case, the zero-current phase advance in x plane is larger than 90◦, which means that the fourth-order particle resonance can be manifested in the transverse plane.
In Fig. 7.23 (a), the emittance exchange betweenxandzis observed along 20 periods. In the range of blue box, both emittance exchange from non-oscillatory parametric instability and the fourth-order particle resonance stop bands are includes. However, the transverse tune depression is too small to excite
the high effects of the fourth-order particle resonance. On the other hand, for longitudinal plane (red line), the fourth-order resonance affects more than the effects of the emittance exchange withxdirection.
Figure 7.23 (b) shows the emittance growth along 100 solenoid focusing periods. As the transverse emittance increases because of the emittance exchange withzdirection as in blue box of Fig. 7.23 (a), beam becomes to be affected more by the fourth-order particle resonance and the envelope instability, resulting in the large emittance growth as shown in the emittance growth plot and phase space plots in x and z planes.
Chapter 8
Design study of Beam Loss Monitoring (BLM) system
A new heavy ion accelerator facility called RAON has been constructed in Daejeon, Korea to produce rare isotope beams of various energies for the Rare Isotope Science Project (RISP). This facility is designed to use both the In-flight Fragmentation (IF) and Isotope Separation On-Line (ISOL) systems to provide a wide range of rare isotope beams to be utilized in many fundamental physics experiments and in various applications. The RAON can use both stable heavy ion beams and rare isotope beams with energies up to a few hundreds of MeV/u with 400 kW of beam power. One of the greatest challenges in operating such a high beam power facility (∼400 kW) is to accurately monitor the beam loss and trigger the Machine Protection System (MPS) reasonably quickly. When the beam loss happens along the beam line component, the lost particles hit the surface of beam pipe and generate neutron and gamma radiations, which can cause the damage on the accelerator facilities. In that reason, it is essential to measure the beam loss-induced radiations along the beam line and stop the machine within the right time.
In this section, we report the conceptual design of beam loss monitoring system for RAON. Monte Carlo simulations using MCNPX simulation code are performed to measure and expect the character- istics of beam loss-induced neutron and gamma radiations. The types of detectors can be determined based on what kind of radiations should be mainly measured according to the diagnostic positions. By considering the sensitivities of the various kinds of detectors, we can predict the possible range of radi- ations to be measured by the detectors and calculate the response time requirements. This design study of beam loss monitoring system in RAON has been reported in Ref. [81].
8.1 Introduction of BLM in RAON
A new heavy ion accelerator facility called RAON has been being constructed in Daejeon, Korea for the Rare Isotope Science Project (RISP) [82]. There are two rare isotope production systems at ROAN: the Isotope Separation On-Line (ISOL) and In-flight Fragmentation (IF) systems. The ISOL system uses
light ion beams (e.g., 70 MeV protons) to hit a high Z nuclear target and the IF system uses heavy ion beams (e.g., 200 MeV/u uranium ions) to hit a low Z nuclear target producing the Rare Isotope Beams (RIBs). At the end of the ISOL and IF systems, various experimental systems such as the Korea Broad acceptance Recoil Spectrometer and Apparatus (KOBRA) and Large Acceptance Multi-Purpose Spec- trometer (LAMPS) have been manufactured [83]. The RAON is expected to play an important role in nuclear physics research by taking advantage of high-intensity RIBs and high performance experimental systems.
Figure 8.1: Layout of the RAON accelerator facility. Low energy stable ions and rare isotope beams are accelerated along the first superconducting linac (SCL3), and are further accelerated along the main driver linac (SCL2) up to 400 kW beam power.
Figure 8.1 shows the overall layout of the RAON accelerator facility [83]. Both heavy ion beams ranging from protons to uranium and RIBs can be generated and delivered through the superconducting linear accelerator (linac) sections. Low energy stable ions or RIBs ranging from a few to 18.5 MeV/u energy can be accelerated along the first superconducting linac (SCL3). Beams can be further acceler- ated through the main driver linac (SCL2), reaching up to a few hundreds of MeV/u with 400 kW beam power.
While the beam is transported through the beam pipe, some lost particles can deviate from the de- signed trajectories along the beam pipe and hit the surface of beam pipe component, which accordingly generates unwanted radiations (see Fig. 1.2). There are two kinds of beam loss generation mechanisms, fast loss and slow loss. Fast losses are primarily caused by the failure of accelerator components, thus they happen unexpectedly and occur instantaneously. By contrast, slow losses primarily arise because of the intrinsic beam transport characteristics, such as halo formations generated from the non-linear space-charge effects [39, 84, 85], which are rather expected situation and occur slowly (these typically accumulate over 100 ms).
One of the greatest challenges in operating a high beam power facility (∼400 kW) is to monitor the beam loss accurately and trigger the machine protection system (MPS) as quickly as possible [86, 87].
The Beam Loss Monitor (BLM) is one of the key elements of the MPS. It is used to protect beam line components from the fast or slow losses, minimize activation of maintenance components, and provide information for beam tuning and optimization.
A BLM primarily detects neutron and gamma radiations, which are generated through interactions
between the lost particles and the atoms in the beam line components. To select and design the most appropriate BLM systems, many accelerator projects have relied on the detailed numerical simulations for calculating the beam loss-induced radiations. There are different kinds of simulation tools, such as GEANT4 [88], MARS [89], FLUKA [90], and MCNPX [91]. In this work, we use MCNPX simulation tool to predict and understand about the beam loss-induced neutron and gamma radiations. This step is helpful for designing proper beam loss detectors after all.