  An interfacial approximation of the streamer stage in the evolution of sparks
and lightning can be written as a Laplacian growth model regularized by a
`kinetic undercooling' boundary condition. We study the linear stability of
uniformly translating circles that solve the problem in two dimensions. In a
space of smooth perturbations of the circular shape, the stability operator is
found to have a pure point spectrum. Except for the zero eigenvalue for
infinitesimal translations, all eigenvalues are shown to have negative real
part. Therefore perturbations decay exponentially in time. We calculate the
spectrum through a combination of asymptotic and series evaluation. In the
limit of vanishing regularization parameter, all eigenvalues are found to
approach zero in a singular fashion, and this asymptotic behavior is worked out
in detail. A consideration of the eigenfunctions indicates that a strong
intermediate growth may occur for generic initial perturbations. Both the
linear and the nonlinear initial value problem are considered in a second
paper.
