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<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">SPACE PHYSICS SEMINAR</span><o:p></o:p></p>
<p class="MsoNormal" align="center" style="text-align:center"> <o:p></o:p></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">DEPARTMENT OF EARTH, PLANETARY, AND SPACE SCIENCES</span><o:p></o:p></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">DEPARTMENT OF ATMOSPHERIC AND OCEANIC SCIENCES</span><o:p></o:p></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">UNIVERSITY OF CALIFORNIA, LOS ANGELES</span><o:p></o:p></p>
<p class="MsoNormal" align="center" style="text-align:center"> <o:p></o:p></p>
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<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">ZOOM LINK PROVIDED BELOW</span><o:p></o:p></p>
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<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue"> </span><a href="https://ucla.zoom.us/j/92101918782?pwd=Z2o5RmI4OEpBWW4zcG1DZStIUWgrZz09" target="_blank">https://ucla.zoom.us/j/92101918782?pwd=Z2o5RmI4OEpBWW4zcG1DZStIUWgrZz09</a><o:p></o:p></p>
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<p align="center" style="margin:0in;text-align:center;font-stretch:normal"><b><span style="color:blue">Charged Particle Isotropization in Collisionless Environments: the Role of Turbulence as well as Very Short Radius-of-Curvature Toroidal Field Geometries<o:p></o:p></span></b></p>
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<b><span style="color:blue"><o:p> </o:p></span></b></p>
<p align="center" style="margin:0in;text-align:center"><i><span style="color:blue">Professor William I. Newman<o:p></o:p></span></i></p>
<p align="center" style="margin:0in;text-align:center;font-stretch:normal"><i><span style="color:blue">Departments of Earth, Planetary, and Space Physics; Physics and Astronomy; and Mathematics<o:p></o:p></span></i></p>
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<p style="margin:0in"><span style="color:blue">The kinematics of individual particles responding to magnetic fields with very short radius-of-curvature R lines of force is highly complex, and the statistical nature of observed kinetic energy partitioning is
often noted as being isotropic. Suppose a charged particle with a velocity v is injected into an environment with an associated gyrofrequency Om where with no electric field present. Northrop (1963) demonstrated, when the dimensionless constant Psi = v/Omega
R << 1, that the behavior would be adiabatic and largely field-aligned. A natural question, then, is how the particle motion would evolve if its kinetic energy were increased making Psi very large. We approach this question in two steps.<o:p></o:p></span></p>
<p style="margin:0in;font-stretch:normal"><span style="color:blue">(a) Consider the situation where the magnetic field undergoes abrupt changes in orientation, as a model for turbulence, intermittently rendering its radius-of-curvature R=0 This produces to
a field configuration that could be described literally as a ``stick-model.'' We show analytically via orbit integration methods in conjunction with Brownian motion methodologies that the particle's velocity distribution becomes isotropic.<o:p></o:p></span></p>
<p style="margin:0in;font-stretch:normal"><span style="color:blue">(b) Consider a toroidally symmetric electric field with radius-of-curvature R as might be encountered in a tokamak or as an approximation to field geometries encountered in space-based observations
as well as their simulations. Schmidt (1979) noted that the associated Hamiltonian is "integrable" and every particle satisfies three conservation laws. He showed that these presented bounds on how the kinetic energy would evolve in time. Others have followed
suit and in some instances presented numerical solutions to illustrate the complex behavior that emerged. However, an explicit analytic solution for the particle trajectories has eluded investigations owing to technical complexities. Exploiting the scaling
properties of the field, we are able obtain analytically the evolution of the field and calculate explicitly how the distribution of its kinetic energy components varies as a function of Psi and become isotropic as Psi becomes infinite, including situations
where the relativistic Lorentz factor must be included. While this latter result employs a specific model for the field geometry, the KAM theory for perturbations to that integrable model provides substantial assurance that its conclusions remain robust in
other toroidal geometries. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:blue"> <o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">Friday, November 12, 2021<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">3:30 - 5:00 PM<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue"> <o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="color:blue">In-Charge: Marco Velli<o:p></o:p></span></p>
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