Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Van Kampen modes for bunch longitudinal motion   Conditions for existence, uniqueness and stability of bunch steady states are
considered. For the existence uniqueness problem, simple algebraic equations
are derived, showing the result both for the action and Hamiltonian domain
distributions. For the stability problem, van Kampen theory is used. Emerging
of discrete van Kampen modes show either loss of Landau damping, or
instability. This method can be applied for an arbitrary impedance, RF shape
and beam distribution function Available areas on intensity-emittance plane are
shown for resistive wall wake and single harmonic, bunch shortening and bunch
lengthening RF configurations.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg