COMMENTS ON C7: : A High Energy, Small Phase-Space Volume Muon Beam

1995 ◽  
pp. 376-388
Keyword(s):  
Phase Space ◽  
High Energy ◽  
Muon Beam ◽  
Phase Space Volume ◽  
Small Phase ◽  
Space Volume

scholarly journals A high energy, small phase-space volume muon beam

1969 ◽  
Vol 69 (1) ◽  
pp. 77-88 ◽  
Author(s):  
J. Cox ◽  
F. Martin ◽  
M.L. Perl ◽  
T.H. Tan ◽  
W.T. Toner ◽  
...  
Keyword(s):  
Phase Space ◽  
High Energy ◽  
Muon Beam ◽  
Phase Space Volume ◽  
Small Phase ◽  
Space Volume

Phase-space volume based control of semibatch reactors

2010 ◽  
Vol 88 (3) ◽  
pp. 320-330 ◽  
Author(s):  
José-Manuel Zaldívar ◽  
Fernanda Strozzi
Keyword(s):  
Phase Space ◽  
Phase Space Volume ◽  
Space Volume

scholarly journals Almost additive entropy

2014 ◽  
Vol 11 (05) ◽  
pp. 1450040 ◽  
Author(s):  
Nikos Kalogeropoulos
Keyword(s):  
Phase Space ◽  
Shannon Entropy ◽  
Power Law ◽  
Physical Significance ◽  
Small Deviations ◽  
Phase Space Volume ◽  
Composition Property ◽  
Flat Manifolds ◽  
Special Case ◽  
Space Volume

We explore consequences of a hyperbolic metric induced by the composition property of the Harvda–Charvat/Daróczy/Cressie–Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter q ≈ 1 from the "ordinary" additive case which is described by the Boltzmann/Gibbs/Shannon entropy. By applying the Gromov/Ruh theorem for almost flat manifolds, we show that such systems have a power-law rate of expansion of their configuration/phase space volume. We explore the possible physical significance of some geometric and topological results of this approach.

scholarly journals Relativistic transformation of phase-space distributions

2011 ◽  
Vol 29 (7) ◽  
pp. 1259-1265 ◽  
Author(s):  
R. A. Treumann ◽  
R. Nakamura ◽  
W. Baumjohann
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Volume Element ◽  
Plasma Parameters ◽  
Astrophysical Plasmas ◽  
Relativistic Case ◽  
Phase Space Volume ◽  
Radiation Theory ◽  
High Mach ◽  
Space Volume

Abstract. We investigate the transformation of the distribution function in the relativistic case, a problem of interest in plasma when particles with high (relativistic) velocities come into play as for instance in radiation belt physics, in the electron-cyclotron maser radiation theory, in the vicinity of high-Mach number shocks where particles are accelerated to high speeds, and generally in solar and astrophysical plasmas. We show that the phase-space volume element is a Lorentz constant and construct the general particle distribution function from first principles. Application to thermal equilibrium lets us derive a modified version of the isotropic relativistic thermal distribution, the modified Jüttner distribution corrected for the Lorentz-invariant phase-space volume element. Finally, we discuss the relativistic modification of a number of plasma parameters.

scholarly journals SHARP SPECTRAL ESTIMATES IN DOMAINS OF INFINITE VOLUME

2011 ◽  
Vol 23 (06) ◽  
pp. 615-641 ◽  
Author(s):  
LEANDER GEISINGER ◽  
TIMO WEIDL
Keyword(s):  
Phase Space ◽  
Dirichlet Boundary ◽  
Semiclassical Limit ◽  
Dirichlet Boundary Conditions ◽  
Bounded Domains ◽  
Infinite Volume ◽  
Uniform Bounds ◽  
Phase Space Volume ◽  
Spectral Estimates ◽  
Space Volume

We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume — and therefore on the volume of the domain — must fail. Here we present a method on how one can nevertheless prove uniform bounds on eigenvalues and eigenvalue means which are sharp in the semiclassical limit.We give examples in horn-shaped regions and so-called spiny urchins. Some results are extended to Schrödinger operators defined on quasi-bounded domains with Dirichlet boundary conditions.

scholarly journals A Family of Hierarchical Symplectic Maps for N-body Simulations with Post-Newtonian Corrections

2017 ◽  
Vol 45 ◽  
pp. 1760021
Author(s):  
Guilherme Gonçalves Ferrari
Keyword(s):  
Phase Space ◽  
Body Problem ◽  
Hamiltonian Dynamics ◽  
Symplectic Maps ◽  
Time Step ◽  
Phase Space Volume ◽  
Time Stepping ◽  
Adaptive Time ◽  
The Individual ◽  
Space Volume

Symplectic maps are well known for preserving the phase-space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times, such as the [Formula: see text]-body problem. However, when combined with a varying time-step scheme, they end up losing its symplecticity and become numerically inefficient. We address this problem by using a recursive Hamiltonian splitting based on the time-symmetric value of the individual time-steps required by the particles in the system. We present a family of 48 quasi-symplectic maps with different orders of convergence (2nd-, 4th- & 6th-order) and three time-stepping schemes: i) 16 using constant time-steps, ii) 16 using shared adaptive time-steps, and iii) 16 using hierarchical (individual) time-steps. All maps include post-Newtonian corrections up to order 3.5PN. We describe the method and present some details of the implementation.

MICE: The International Muon Ionisation Cooling Experiment

2005 ◽  
Vol 20 (16) ◽  
pp. 3843-3846
Author(s):  
◽  
Malcolm Ellis
Keyword(s):  
Phase Space ◽  
High Energy ◽  
Muon Beam ◽  
Cooling Channel ◽  
Rutherford Appleton Laboratory ◽  
Rf Cavities ◽  
Demonstration Experiment ◽  
Muon Lifetime ◽  
Space Compression ◽  
And Storage

Muon storage rings have been proposed for use as sources of intense high-energy neutrino beams and as the basis for multi-TeV lepton-antilepton colliding beam facilities. To optimise the performance of such facilities is likely to require the phase-space compression (cooling) of the muon beam prior to acceleration and storage. The short muon-lifetime makes it impossible to employ traditional techniques to cool the beam while maintaining the muon-beam intensity. Ionisation cooling, a process in which the muon beam is passed through a series of liquid hydrogen absorbers followed by accelerating RF-cavities, is the technique proposed to cool the muon beam. The international Muon Ionisation Cooling Experiment (MICE) collaboration has been formed to carry out a muon-cooling demonstration experiment, and its proposal to Rutherford Appleton Laboratory has been approved. The MICE cooling channel, the instrumentation and the implementation at the Rutherford Appleton Laboratory is described together with the predicted performance of the channel and the measurements that will be made.

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