Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational Self-Consistent Theory for Beam-Loaded Cavities   A new variational theory is presented for beam loading in microwave cavities.
The beam--field interaction is formulated as a dynamical interaction whose
stationarity according to Hamilton's principle will naturally lead to
steady-state solutions that indicate how a cavity's resonant frequency, $Q$ and
optimal coupling coefficient will detune as a result of the beam loading. A
driven cavity Lagrangian is derived from first principles, including the
effects of cavity wall losses, input power and beam interaction. The general
formulation is applied to a typical klystron input cavity to predict the
appropriate detuning parameters required to maximize the gain (or modulation
depth) in the average Lorentz factor boost, $\langle \Delta\gamma \rangle$.
Numerical examples are presented, showing agreement with the general detuning
trends previously observed in the literature. The developed formulation carries
several advantages for beam-loaded cavity structures. It provides a
self-consistent model for the dynamical (nonlinear) beam--field interaction, a
procedure for maximizing gain under beam-loading conditions, and a useful set
of parameters to guide cavity-shape optimization during the design of
beam-loaded systems. Enhanced clarity of the physical picture underlying the
problem seems to be gained using this approach, allowing straightforward
inclusion or exclusion of different field configurations in the calculation and
expressing the final results in terms of measurable quantities. Two field
configurations are discussed for the klystron input cavity, using finite
magnetic confinement or no confinement at all. Formulating the problem in a
language that is directly accessible to the powerful techniques found in
Hamiltonian dynamics and canonical transformations may potentially carry an
additional advantage in terms of analytical computational gains, under suitable
conditions.

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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org