Chaotic particle heating due to an obliquely propagating wave in a magnetized plasma.

We study the dynamics of a relativistic charged particle in the presence of a uniform magnetic field and a stationary electrostatic wave that propagates at an arbitrary angle. The wave is considered as a series of periodic pulses which allows us to derive an exact map for the system. In particular, we investigate the heating process of an initially low-energy particle. It is found that abrupt changes in the maximum energy attained by the particle may occur as the angle between the wave propagation and the magnetic field varies. To determine what is the mechanism behind this phenomenon a reduced Hamiltonian that retains the important dynamical features is obtained. Using both Poincaré plots and perturbation theory, we identify that a separatrix reconnection is the key mechanism for the abrupt change in particle response.

Alternate islands of multiple isochronous chains in wave-particle interactions.

We analyze the dynamics of a relativistic particle moving in a uniform magnetic field and perturbed by a standing electrostatic wave. We show that a pulsed wave produces an infinite number of perturbative terms with the same winding number, which may generate islands in the same region of phase space. As a consequence, the number of isochronous island chains varies as a function of the wave parameters. We observe that in all the resonances, the number of chains is related to the amplitude of the various resonant terms. We determine analytically the position of the periodic points and the number of island chains as a function of the wave number and wave period. Such information is very important when one is concerned with regular particle acceleration, since it is necessary to adjust the initial conditions of the particle to obtain the maximum acceleration.

Controlling chaos in wave-particle interactions.

We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos from spreading to large regions, making the controlled dynamics more regular. We show numerically that the control term just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration.

Standard map in magnetized relativistic systems: fixed points and regular acceleration.

We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.

Equilibrium and stability of off-axis periodically focused particle beams.

A general equation for the centroid motion of free, continuous, intense beams propagating off axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. The properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed.

Correlation decay and partial coherence in nonlinear wave interactions.

In the present analysis we study the broad-band triplet interaction in regimes of large amplitudes. Linear response theories associated with nonlinear arguments are used to show that even though coherence of high-frequency modes is lost as one first encounters chaotic regimes, it can be restored as field amplitudes grow further. We discuss implications of the feature for fixed-phase interactions.

Gap bifurcations in nonlinear dynamical systems.

We investigate the dynamics generated by a type of equation which is common to a variety of physical systems where the undesirable effects of a number of self-consistent nonlinear forces are balanced by an externally imposed controlling harmonic force. We show that the equation presents a new sequence of bifurcations where periodic orbits are created and destroyed in such a nonsimultaneous way that may leave the appropriate phase-space occasionally empty of fundamental harmonic orbits and confined trajectories. A generic analytical model is developed and compared with a concrete physical example.

Nonlinear dynamics of periodically focused intense particle beams.

We extend a previous study [R. Pakter and F. B. Rizzato, Phys. Rev. Lett. 87, 044801 (2001)] and investigate the nonlinear dynamics of periodically focused intense particle beams. We show that (i) the scenario as the focusing field increases is not the existence of a single threshold above which stable matched (equilibrium) solutions are absent, as believed so far, but the existence of successive regions of stability interrupted by gaps where periodic solutions are either unstable or simply do not exist; (ii) the beam can be focused to tighter radii using stable matched solutions found for focusing field strengths greater than the previous threshold. A comprehensive analysis is carried out as a function of the relevant parameters of the system. Self-consistent simulations validate the findings. The gaps are of crucial importance because they must be avoided if the goal is beam confinement with matched solutions; we develop an analytical model to determine the gap structure, which agrees well with computer simulations.

Stability of periodically focused intense particle beams.

A stability analysis of periodically focused intense particle beams based on the beam envelope equation is performed. We show that (i) the scenario, as the focusing field increases, is not the existence of a single threshold above which stable matched (equilibrium) solutions are absent, as generally believed, but the existence of successive regions of stability interrupted by gaps of instability; (ii) the beam can be focused to tighter radii using new stable matched solutions found for focusing field strengths greater than the previous threshold. Self-consistent simulations validate the findings.

Cold-fluid equilibrium for a corkscrewing elliptic beam in a variably focusing channel

It is shown that there exists a new class of cold-fluid corkscrewing elliptic beam equilibria for ultrahigh-brightness, space-charge-dominated beam propagation through a linear focusing channel consisting of uniform solenoidal, periodic solenoidal, and/or alternating-gradient quadrupole focusing magnets in an arbitrary arrangement including field tapering. The equilibrium beam density and flow velocity profiles and equilibrium self-electric and self-magnetic fields are determined by solving generalized beam envelope equations. In proper limits, such cold-fluid corkscrewing elliptic beam equilibria recover many familiar beam equilibria in beam physics, including the round rigid-rotor Vlasov beam equilibria in uniform and periodic solenoidal focusing fields and the Kapchinskij-Vladimirskij beam equilibrium in an alternating-gradient quadrupole focusing field. For beams with negligibly small emittance, the equilibrium solutions are validated with self-consistent simulations. Examples and applications of the present equilibrium beam theory are discussed. As an important application of the present equilibrium beam theory, a general technique is developed and demonstrated with an example to control large-amplitude density and flow velocity fluctuations (such as beam hollowing and halo formation) often observed in ultrahigh-brightness beams.

Chaos and coherence in the conservative three-mode decay interaction

In this work we analyze the influence of chaos on the coherence of the mismatched three-wave interaction. Chaos starts to play a decisive role in the problem when adiabatic approximations leading to an integrable model for the system cease to be valid. In regular regimes where the field levels are sufficiently small, there is a characteristic value for the frequency mismatch of the triplet below which coherence and phase locking are dominant. In chaotic regimes, on the other hand, there is no such value and locking behaves in a more complicated way.

Hemangioma of the bladder: sonographic and computerized tomography findings.

We report a bladder hemangioma in a patient with the Klippel-Trenaunay syndrome. Ultrasound findings consisted of a markedly thickened bladder wall with multiple serpiginous, anechoic spaces. Computerized tomography demonstrated diffuse bladder wall thickening with foci of calcification.

Diffuse arterial narrowing as a result of intimal proliferation: a delayed complication of embolectomy with the Fogarty balloon catheter.

Most complications of embolectomy with the Fogarty balloon catheter are recognized early and have received ample attention in the surgical and radiologic literature. However, the delayed complication of diffuse arterial narrowing causing severe ischemia has received little emphasis, perhaps because follow-up arteriography is not always performed. This report describes five patients--women 43 to 62 years of age--with progressive leg ischemia discovered 2 to 4 months after embolectomy with the balloon catheter. Angiography showed a characteristic pattern of severe, smooth narrowing of that portion of the artery in which balloon embolectomy was performed. Pathologic examination of arterial specimens, available in two of the five patients, revealed marked intimal cellular proliferation, which narrowed the arteries severely without evidence of thrombosis, significant atheromatosis, or active arteritis. The cause appears to be intimal damage by the balloon. Embolectomy with the balloon catheter should be done especially carefully in relatively young women.

Hepatoblastoma: radiologic-pathologic correlation in 50 cases.

Fifty cases of hepatoblastoma were reviewed. Virtually all patients were infants or young children with hepatomegaly or a mass. Calcification seen on 11 of 20 radiographs was often in a pattern of small chunks, and eight of these correlated with osteoid formation in histologically mixed hepatoblastomas. Angiography generally showed tumor vascularity, sometimes with a spoke-wheel pattern. Suggestion of tumor nodularity or lobulation on sonography or computed tomography (CT) correlated with the gross appearance. The tumor was usually echogenic and occasionally had small hypoechoic or anechoic areas representing necrosis or hemorrhage. On CT it was usually hypodense, with minimal if any enhancement. The calcification pattern and demonstration of tumor lobulation with septation may help differentiate hepatoblastoma from other liver neoplasms in infants and children under 5 years of age.

CT findings in splenic hemangiomas in the Klippel-Trenaunay-Weber syndrome.

The Klippel-Trenaunay-Weber syndrome consists of cutaneous port wine hemangiomas, superficial venous varicosities, and soft tissue and bony hypertrophy of an extremity. We describe three patients with this syndrome with hypodense lesions in the spleen which in one case became isodense after bolus contrast CT. In one case ultrasound found numerous echopenic and echogenic masses. These lesions are presumed to represent multiple hemangiomata.

Calf hematoma--computed tomographic and magnetic resonance findings.

Four patients with hematomas of the calf are presented. The diagnosis was made by computed tomography (CT) in three cases and CT/magnetic resonance imaging (MRI) in one case. In all cases, CT or MRI clarified a confusing clinical picture. CT and MRI can help differentiate the types of calf mass (i.e., hematoma, tumor, Baker cyst, thrombophlebitis) and assist proper clinical management in a rapid, noninvasive fashion.