Modesto Pusterla

Quantum-like approach to the transversal and longitudinal beam dynamics. The halo problem

Abstract: An interpretation of the formation of halo in accelerators based on quantum-like theory by a diffraction model is given in terms of the transversal beam motion. Physical implications of the longitudinal dynamics are also examined.

Lévy processes and Schrödinger equation

We analyze the extension of the well known relation between Brownian motion and the Schrodinger equation to the family of the Levy processes. We consider a Levy–Schrodinger equation where the usual kinetic energy operator–the Laplacian–is generalized by means of a selfadjoint, pseudodifferential operator whose symbol is the logarithmic characteristic of an infinitely divisible law. The Levy–Khintchin formula shows then how to write down this operator in an integro-differential form. When the underlying Levy process is stable we recover as a particular case the fractional Schrodinger equation. A few examples are finally given and we find that there are physically relevant models–such as a form of the relativistic Schrodinger equation–that are in the domain of the non stable Levy–Schrodinger equations.

Quantum approach to the halo formation in high current beams

Abstract An interpretation of the formation of halo in accelerators based on quantum-like theory by a diffraction model is given in terms of the transversal beam motion. Physical implications of the longitudinal dynamics are also examined.

A study of effects of tune modulation in nonlinear maps

A simple model of betatronic dynamics is studied in which a modulation in tune is present, in order to describe the noise in a magnet power supply. Analytical and numerical results are presented.

The Relativistic Stern-Gerlach Interaction and Quantum Mechanics Implications

The time varying relativistic Stern‐Gerlach force, which acts over a charged particle endowed with a magnetic moment, is deduced from the Dirac Hamiltonian finding its coincidence with the classical expression. Possible drawbacks related to the Heisenberg uncertainty principle are discussed.

MASS SPECTRUM FROM STOCHASTIC LÉVY-SCHRÖDINGER RELATIVISTIC EQUATIONS: POSSIBLE QUALITATIVE PREDICTIONS IN QCD

Starting from the relation between the kinetic energy of a free Levy–Schrodinger particle and the logarithmic characteristic of the underlying stochastic process, we show that it is possible to get a precise relation between renormalizable field theories and a specific Levy process. This subsequently leads to a particular cutoff in the perturbative diagrams and can produce a phenomenological mass spectrum that allows an interpretation of quarks and leptons distributed in the three families of the standard model.

Relativistic Stern-Gerlach Interaction in an RF Cavity

The general expression of the Stern-Gerlach force is deduced for a relativistic charged spin2 particle which travels inside a time varying magnetic field. This result was obtained either by means of two Lorentz boosts or starting from Dirac’s equation. Then, the utilization of this interaction for attaining the spin states separation is reconsidered in a new example using a new radio-frequency arrangement. 1 The Relativistic Stern-Gerlach Force The time varying Stern-Gerlach, SG, interaction of a relativistic fermion with an e.m. wave has been proposed to separate beams of particles with opposite spin states corresponding to different energies[1]. We will show how spin polarized particle will exchange energy with the electromagnetic field of an RF resonator. Let us denote with (x, y, z) the coordinates of a particle in the laboratory, and with (x, y, z) the coordinates in the particle rest frame, PRF. In the latter the SG force that represents the action of an inhomogeneous magnetic field on a particle endowed with a magnetic moment ~μ is ~ f ′ SG = ∇′(~μ∗ · ~ B) = ∂ ∂x (~μ · ~ B)x̂ + ∂ ∂y (~μ · ~ B)ŷ + ∂ ∂z (~μ · ~ B)ẑ (1) with ~μ = g e 2m ~ S. (2) Here e is the elementary charge with “ + ” for protons and positrons, p, e, and ′′ = for antiprotons and electrons, p̄, e, making ~μ and ~ S either parallel or antiparallel to 1 each other, respectively. m is the rest mass of the particle, g the gyromagnetic ratio and a the anomaly defined as a = g−2 2 = 

The Relativistic Stern‐Gerlach Interaction as a Tool for Attaining the Spin Separation

The relativistic Stern‐Gerlach interaction is here considered as a tool for obtaining the spin state separation of an unpolarized (anti)proton beam circulating in a ring. Drawbacks, such as spin precessions within the TE rf cavity, spurious kicks due to the transverse electric field and, worst of all, filamentation in the longitudinal phase plane are analyzed. Possible remedies are proposed and their feasibility is discussed.

Stern-Gerlach interaction in fermion beams

The Stern-Gerlach interaction, between a moving charged particle endowed with a magnetic moment and a radio-frequency e.m. field, is studied by means of a semi-classical approach. Theoretical results are presented, and a possible experimental check of this theory is discussed.