One-dimensional kinetic description of nonlinear traveling-pulse (soliton) and traveling-wave disturbances in long coasting charged particle beams

This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius $r_{w}$. The average axial electric field is expressed as $\langle E_{z}\rangle=-(\partial/\partial z)\langle\phi\rangle=-e_{b}g_{0}\partial\lambda_{b}/\partial z-e_{b}g_{2}r_{w}^{2}\partial^{3}\lambda_{b}/\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $\lambda_{b}(z,t)=\int dp_{z}F_{b}(z,p_{z},t)$ is the line density of beam particles, and $F_{b}(z,p_{z},t)$ satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (solitons) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (a) the nonlinear waterbag distribution, where $F_{b}=const.$ in a bounded region of $p_{z}$-space; and (b) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field $\langle E_{z}\rangle$. .Comment: 42 pages, 17 figure

Analytical Solutions for the Nonlinear Longitudinal Drift Compression (Expansion) of Intense Charged Particle Beams

To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics

Negotiated Development Denial Meets People\u27s Court: Del Monte Dunes Brings New Wildcards to Exactions Law

The United States Supreme Court Answered YES to the $1.45 million over exaction question for 1999. In City of Monterey v. Del Monte Dunes at Monterey Ltd., a unanimous court extended the scope of compensatory takings review beyond land dedication conditions into the realm of regulatory denial. Justice Kennedy\u27s opinion vitalized the legitimate state interests test from Agins v. City of Tiburon to sustain an inverse condemnation conclusion and damage award to the frustrated developer. A majority of the court also concurred that the trial court may delegate this takings conclusion to the jury under federal civil rights law. The activation of Agins\u27 substantive takings test in such challenges and the prospect of continued lay application of constitutional law to development restrictions add uncertain dimensions to exactions litigation at the millennium. In Del Monte Dunes, the Court also distinguished the instant development denial of an inverse condemnation claim from the land dedication conditions at issue in Dolan v. City of Tigard. This distinction enabled the unanimous Court to uphold the trial verdict based on Agins and avoid elements of the Ninth Circuit\u27s reasoning invoking the Dolan rough proportionality test. Other recent federal and state decisions also decline to extend Dolan\u27s applicability beyond individual land dedication development conditions to other forms of economic exactions. This year\u27s exactions and impact fee report focuses on Del Monte Dunes, namely its effects on negotiated development, trial practice, and on regulatory takings doctrine as defined by judges and juries in civil rights litigation

Negotiated Development Denial Meets People\u27s Court: Del Monte Dunes Brings New Wildcards to Exactions Law

The United States Supreme Court Answered YES to the $1.45 million over exaction question for 1999. In City of Monterey v. Del Monte Dunes at Monterey Ltd., a unanimous court extended the scope of compensatory takings review beyond land dedication conditions into the realm of regulatory denial. Justice Kennedy\u27s opinion vitalized the legitimate state interests test from Agins v. City of Tiburon to sustain an inverse condemnation conclusion and damage award to the frustrated developer. A majority of the court also concurred that the trial court may delegate this takings conclusion to the jury under federal civil rights law. The activation of Agins\u27 substantive takings test in such challenges and the prospect of continued lay application of constitutional law to development restrictions add uncertain dimensions to exactions litigation at the millennium. In Del Monte Dunes, the Court also distinguished the instant development denial of an inverse condemnation claim from the land dedication conditions at issue in Dolan v. City of Tigard. This distinction enabled the unanimous Court to uphold the trial verdict based on Agins and avoid elements of the Ninth Circuit\u27s reasoning invoking the Dolan rough proportionality test. Other recent federal and state decisions also decline to extend Dolan\u27s applicability beyond individual land dedication development conditions to other forms of economic exactions. This year\u27s exactions and impact fee report focuses on Del Monte Dunes, namely its effects on negotiated development, trial practice, and on regulatory takings doctrine as defined by judges and juries in civil rights litigation