Pavel Snopok

HIGH-ORDER DESCRIPTION OF THE DYNAMICS IN FFAGs AND RELATED ACCELERATORS

In this paper, we describe newly developed tools for the study and analysis of the dynamics in FFAG accelerators based on transfer map methods unique to the code COSY INFINITY. With these new tools, closed orbits, transverse amplitude dependencies and dynamic aperture are determined inclusive of full nonlinear fields and kinematics to arbitrary order. The dynamics are studied at discrete energies, via a high-order energy-dependent transfer map. The order-dependent convergence in the calculated maps allows precise determination of dynamic aperture and detailed particle dynamics. Using normal form methods, and minimal impact symplectic tracking, amplitude- and energy-dependent tune shifts and resonance strengths are extracted. Optimization by constrained global optimization methods further refine and promote robust machine attributes. Various methods of describing the fields will be presented, including representation of fields in radius-dependent Fourier modes, which include complex magnet edge contours and superimposed fringe fields, as well as the capability to interject calculated or measured field data from a magnet design code or actual components, respectively.

RECENT PROGRESS ON THE 6D COOLING SIMULATIONS IN THE GUGGENHEIM CHANNEL

The RFOFO ring is considered to be one of the most promising six-dimensional cooling channels proposed for the future muon collider. It has a number of advantages over other cooling channels, but it also has certain drawbacks. The injection and extraction issue as well as the absorber overheating are its main problems. In this article the simulations of a possible solution to these problems, the RFOFO helix, commonly referred to as the Guggenheim channel, are studied in detail. The details of the tracking studies of both the idealized and realistic lattices are presented and compared to the performance of the underlying RFOFO cooling ring design.

Simulation and Optimization of the Tevatron Accelerator

The Tevatron accelerator, currently the particle accelerator with the highest energy in the world, consists of a ring with circumference of four miles in which protons are brought into collision with antiprotons at speeds very close to the speed of light. The accelerator currently under development at Fermilab represents a significant upgrade, but experienced significant limitations during initial operation. The correction of some of the problems that appeared using techniques of automatic differentiation are described. The skew quadrupole correction problems are addressed in more detail, and different schemes of correction are proposed.

Isochronous (CW) non-scaling FFAGs: Design and simulation

The drive for higher beam power, high duty cycle, and reliable beams at reasonable cost has focused international attention and design effort on fixed field accelerators, notably Fixed‐Field Alternating Gradient accelerators (FFAGs). High‐intensity GeV proton drivers encounter duty cycle and space‐charge limits in the synchrotron and machine size concerns in the weaker‐focusing cyclotrons. A 10–20 MW proton driver is challenging, if even technically feasible, with conventional accelerators—with the possible exception of a SRF linac, which has a large associated cost and footprint. Recently, the concept of isochronous orbits has been explored and developed for nonscaling FFAGs using powerful new methodologies in FFAG accelerator design and simulation. The property of isochronous orbits enables the simplicity of fixed RF and, by tailoring a nonlinear radial field profile, the FFAG can remain isochronous beyond the energy reach of cyclotrons, well into the relativistic regime. With isochronous orbits, the machine proposed here has the high average current advantage and duty cycle of the cyclotron in combination with the strong focusing, smaller losses, and energy variability that are more typical of the synchrotron. This paper reports on these new advances in FFAG accelerator technology and presents advanced modeling tools for fixed‐field accelerators unique to the code COSY INFINITY.The drive for higher beam power, high duty cycle, and reliable beams at reasonable cost has focused international attention and design effort on fixed field accelerators, notably Fixed‐Field Alternating Gradient accelerators (FFAGs). High‐intensity GeV proton drivers encounter duty cycle and space‐charge limits in the synchrotron and machine size concerns in the weaker‐focusing cyclotrons. A 10–20 MW proton driver is challenging, if even technically feasible, with conventional accelerators—with the possible exception of a SRF linac, which has a large associated cost and footprint. Recently, the concept of isochronous orbits has been explored and developed for nonscaling FFAGs using powerful new methodologies in FFAG accelerator design and simulation. The property of isochronous orbits enables the simplicity of fixed RF and, by tailoring a nonlinear radial field profile, the FFAG can remain isochronous beyond the energy reach of cyclotrons, well into the relativistic regime. With isochronous orbits, the ma...

A new lattice design for a 1.5 TeV CoM Muon Collider consistent with the tevatron tunnel

A recent effort is underway to design an efficient match of a Muon Collider to the Fermilab site, potentially using the Tevatron tunnel after decommissioning. This work represents a new design for such a collider with emphasis on shortened IR and systematic high-order correction and dynamics studies. With a 1 cm beta*, simultaneous control of geometric and chromatic aberrations is critical and can only be achieved through the deliberate addition of nonlinear fields in the Interaction Region itself. This work studies both the correction schemes and the unavoidable impact of high-order correctors - sextupoles, octupoles and even duodecapoles - located in the Interaction Region close to the low-beta quadrupoles or focusing elements. This study proposes and systematically addresses the aberrations for different systems of nonlinear correctors and optimizes performance of an advanced IR.

ADVANCES IN NONLINEAR NON-SCALING FFAGs

Accelerators are playing increasingly important roles in basic science, technology, and medicine. Ultra high-intensity and high-energy (GeV) proton drivers are a critical technology for accelerator-driven sub-critical reactors (ADS) and many HEP programs (Muon Collider) but remain particularly challenging, encountering duty cycle and space-charge limits in the synchrotron and machine size concerns in the weaker-focusing cyclotrons; a 10–20 MW proton driver is not presently considered technically achievable with conventional re-circulating accelerators. One, as-yet, unexplored re-circulating accelerator, the Fixed-field Alternating Gradient or FFAG, is an attractive alternative to the other approaches to a high-power beam source. Its strong focusing optics can mitigate space charge effects and achieve higher bunch charges than are possible in a cyclotron, and a recent innovation in design has coupled stable tunes with isochronous orbits, making the FFAG capable of fixed-frequency, CW acceleration, as in the classical cyclotron but beyond their energy reach, well into the relativistic regime. This new concept has been advanced in non-scaling nonlinear FFAGs using powerful new methodologies developed for FFAG accelerator design and simulation. The machine described here has the high average current advantage and duty cycle of the cyclotron (without using broadband RF frequencies) in combination with the strong focusing, smaller losses, and energy variability that are more typical of the synchrotron. The current industrial and medical standard is a cyclotron, but a competing CW FFAG could promote a shift in this baseline. This paper reports on these new advances in FFAG accelerator technology and presents advanced modeling tools for fixed-field accelerators unique to the code COSY INFINITY.1

CALCULATION OF NONLINEAR TUNE SHIFT USING BEAM POSITION MEASUREMENT RESULTS

The calculation of the nonlinear tune shift with amplitude based on the results of measurements and the linear lattice information is discussed. The tune shift is calculated based on a set of specific measurements and some extra information which is usually available, namely that about the size and particle distribution in the beam and the linear optics effect on the particles. The method to solve this problem uses the technique of normal form transformation. The proposed model for the nonlinear tune shift calculation is compared to both the numerical results for the nonlinear model of the Tevatron accelerator and the independent approximate formula for the tune shift by Meller et al. The proposed model shows a discrepancy of about 2%.

Simulated Measurements of Cooling in Muon Ionization Cooling Experiment

Cooled muon beams set the basis for the exploration of physics of flavour at a Neutrino Factory and for multi-TeV collisions at a Muon Collider. The international Muon Ionization Cooling Experiment (MICE) measures beam emittance before and after an ionization cooling cell and aims to demonstrate emittance reduction in muon beams. In the current MICE Step IV configuration, the MICE muon beam passes through low-Z absorber material for reducing its transverse emittance through ionization energy loss. Two scintillating fiber tracking detectors, housed in spectrometer solenoid modules upstream and downstream of the absorber are used for reconstructing position and momentum of individual muons for calculating transverse emittance reduction. However, due to existence of non-linear effects in beam optics, transverse emittance growth can be observed. Therefore, it is crucial to develop algorithms that are insensitive to this apparent emittance growth. We describe a different figure of merit for measuring muon cooling which is the direct measurement of the phase space density.

Optics of Ionization Cooling Channels Under the Influence of Space Charge

Lepton colliders have a significant advantage over their hadron counterparts in that hadron collisions are inefficient and complicated by secondary quark interactions. A muon collider could be used for high energy studies of lepton collisions without the limitations on energy due to synchrotron radiation. The muon beam is produced by sending protons through a target, producing pions which in turn decay into muons with a large momentum spread. For a muon collider, the six-dimensional (6D) phase space volume of the muon beam must be reduced to accelerate it further for injection into a storage ring. Ionization cooling is currently the only feasible method for cooling the beam within a muon lifetime of 2.2 μs. One key technical challenge for a muon collider is the demonstration of the process of ionization cooling. In order for a full 6D ionization cooling experiment to be constructed, a baseline lattice design has to be studied and selected based on detailed simulations [1].

Advanced simulation tools for muon-based accelerators

New software tools are being developed incorporating the most accurate theoretical calculations and experimental data available for crucial and not-yet-considered physics processes specific to muon accelerators. This will substantially enhance the confidence that the tools used in assessing the feasibility of a muon collider or a neutrino factory accurately represent the performance of a real machine. Current status and progress are reported.