Development of the Electron Cooling Simulation Program for JLEIC

In the JLab Electron Ion Collider (JLEIC) project the traditional electron cooling technique is used to reduce the ion beam emittance at the booster ring, and to compensate the intrabeam scattering effect and maintain the ion beam emittance during collision at the collider ring. A new electron cooling process simulation program has been developed to fulfill the requirements of the JLEIC electron cooler design. The new program allows the users to calculate the electron cooling rate and simulate the cooling process with either DC or bunched electron beam to cool either coasting or bunched ion beam. It has been benchmarked with BETACOOL in aspect of accuracy and efficiency. In typical electron cooling process of JLEIC, the two programs agree very well and we have seen a significant improvement of computational speed using the new one. Being adaptive to the modern multicore hardware makes it possible to further enhance the efficiency for computationally intensive problems. The new program is being actively used in the electron cooling study and cooler design for JLEIC. We will present our models and some simulation results in this paper.. JLEIC COOLING SCHEME To reach the frontier in Quantum Chromodynamics, the JLab Electron Ion Collider (JLEIC) will provide an electron beam with energy up to 10 GeV, a proton beam with energy up to 100 GeV, and heavy ion beams with corresponding energy per nucleon with the same magnetic rigidity. The center-of-mass energy goes up to 70 GeV. Two detectors, a primary one with full acceptance and a high-luminosity one with less demanding specification, are proposed. To achieve the ultrahigh luminosity close to 1034 cm-2s-1 per detector with large acceptance, the traditional electron cooling will be implemented strategically. [1] The JLEIC ion complex consists of ion sources, an SRF linac, a booster ring and a collider ring, as shown in Fig 1. Since the electron cooling time is in proportion to the energy and the 6D emittance of the ion beam, which means it is easier to reduce the emittance at a lower energy, a multi-stage cooling scheme has been developed. A low energy DC cooler will be installed at the booster ring, which will reduce the emittance to the desired value for ion beams with the kinetic energy of 2 GeV/u. A bunched beam cooler will be installed at the collider ring, which helps to compensate the intrabeam scattering (IBS) effect and maintain the emittance of the ion beam during the injection process and during the collisions. Figure 1: Components of JLEIC ion complex. CODE DEVELOPMENT GOALS The DC cooler is within the state-of-art. [2] But the bunched beam cooler is out of the state-of-art and needs significant R&D. Numerical simulation is inevitable for the design and optimization of the JLEIC electron cooling system. BETACOOL has been used in our preliminary study and it has successfully supported the JLEIC design. As the study goes more in-depth, it will be beneficial to have a more efficient and more flexible tool to fulfil some specific needs of JLEIC. The goal of this new simulation program is to enhance the simulation capability for electron cooling in JLEIC project. It will preferentially fulfil the needs of JLEIC design. The program simulates the evolution of the macroscopic beam parameters, such as emittances, momentum spread and bunch length, in different electron cooling scenarios: DC cooling, bunched electron to bunched ion cooling, bunched electron to coasting ion cooling, etc. Since BETACOOL has provided a collection of physical models for various electron cooling simulations [3], we decided to follow the models in BETACOOL, whenever they are applicable, and revise them when necessary. We also want to improve the efficiency by strategical arrangement of the calculation and/or by implementation of the models on modern multicore platform. IBS AND ELECTRON COOLING RATE The intrabeam scattering (IBS) effect can cause significant increase of the emittance of the ion beam, due to the high intensity of them, in MEIC in a short time, which ruins the luminosity of the collider. The emittance change rate due to the IBS effect can be calculated using several different formulas under different assumption of ___________________________________________ * Work supported by the Department of Energy, Laboratory Directed Research and Development Funding, under Contract No. DE AC05 06OR23177. # [email protected] Proceedings of IPAC2016, Busan, Korea WEPMW014 01 Circular and Linear Colliders A19 Electron-Hadron Colliders ISBN 978-3-95450-147-2 2451 C op yr ig ht © 20 16 C C -B Y3. 0 an d by th e re sp ec tiv e au th or s • • --c:E-,i~~-,?'-Tc-o".:'-: ol;-;i_ng ion SRF sources Linac Booster medium energy collider ring the ion beam profile and lattice parameters. [4-7] Here we choose Martini model [5] for the IBS rate calculation for JLEIC. Martini model assumes Gaussian distribution for the ion beam, which is reasonable at least for the first order, and the absence of vertical dispersion of the lattice, which is true for JLEIC booster ring and collider ring. The electron cooling rate is defined as the emittance change in a unit time due to the electron cooling effect. We borrow two models from BETACOOL for electron cooling rate calculation: the single particle model and the Monte Carlo model. Using the single particle model, the ion beam will be sampled as a group of ions distributed evenly in the ellipsoid of the given emittance in the phase space. Using the Monte Carlo model, the ion beam will be sampled as a Gaussian bunch whose rms size is determined by the given emittance and the TWISS parameter at the cooler. The friction force on each ion will be calculated. Assuming the friction force is constant while the ion passes through the cooler, the change of momentum of each ion can be calculated. Then the new emittance and the change rate of the emittance can be calculated statistically. Although there are different formulas for friction force calculation, currently we only implement the Parkhomchuk formula in the program, because both the coolers for JLEIC are magnetized. During the injection from the booster ring to the collider ring, the bunched beam cooler will be used to compensate the IBS effect of the coasting ion beam. Coasting ion beam is sometimes modelled as ions on one cross section of the beam [3] under the assumption that the coasting beam is homogeneous in the ring. Such a model works well for DC cooling. But it ignores the variance of the longitudinal electron distribution for bunched electron beam, since the sample ions can only see a slice of the electron beam. Another way is to put the sample ions all along the ring. [3] The circumference of the JLEIC collider ring is more than 2000 m, while the rms length of the electron bunch is only around 2 cm. For JLEIC collider ring, it is not efficient to put the ions all around the ring, since most of the ions do not see the electrons. Assuming all the electron bunches are identical, one only needs to sample the coasting ion beam around the electron bunch, as shown in Fig. 2. A duty factor is defined as D = Ls/Ld, where Ls is the length of the sample area and Ld is the distance between two electron bunch. The cooling rate of the whole coasting ion beam is calculated as the multiplication of the cooling rate of the sample area and the duty factor. This model assumes the cooling effect is distributed evenly among the ions by diffusion. The electron bunch profile could be taken into account using this model. Figure 2: Model of ion beam cooled by electron bunch. ELECTRON COOLING DYNAMICS The evolution of the ion beam under the IBS effect and/or electron cooling effect is simulated by a four-step procedure, which can be described as follows: (1) initialize the computational environment; (2) create the sample ions, (3) calculate the IBS rate and the electron cooling rate, and (4) update the beam parameters, such as emittance, momentum spread, and/or bunch length, update the sample ions, and repeat from (3). Two methods in BETACOOL for electron cooling dynamic simulation, the RMS dynamics method and the model beam method, fit into the four-step procedure. Using the RMS dynamics method, one assumes the ion beam maintains the Gaussian distribution during the cooling process. In step (2), the sample ions with Gaussian distribution is created according the given beam parameters. In step (3), the total emittance change rate 1/�, as the summation of the IBS expansion rate and the electron cooling rate, is calculated. In step (4) the new emittance after cooling is calculated as ��+1 = �� ⋅ ��/�, where � is the time step, ��+1 and �� are emittances at the end and the beginning of the step. Then new sample ions are created according to the new beam parameters. Using the model beam method, one creates a group of ions as the sample of the ion beam at the step (2). IBS rate and/or the cooling rate are/is calculated in step (3). In step (4), the IBS effect is treated as a random kick to each ion, which leads to a change of the momentum. Friction force of electron cooling also changes the momentum. Besides these two effects, each ion also makes a random phase advance during the time interval. Once the 6D coordinates of the sample ions are updated, the new beam parameters can be calculated. Using the model beam method, one can simulate the evolution of the ion beam distribution during the electron cooling process. For example, under a strong electron cooling effect the ion distribution often deviates from Gaussian, which has been observed in experiments, because the center of the ion beam obtains stronger cooling effect than the edge. In such a case, the model beam method is preferred. For more details about these two models, please refer to [3].