  Spatio-temporal evolution of large amplitude upper hybrid oscillations in a
cold homogeneous plasma in the presence of an inhomogeneous magnetic field is
studied analytically and numerically using the Dawson sheet model. It is
observed that the inhomogeneity in magnetic field which causes the upper hybrid
frequency to acquire a spatial dependence, results in phase mixing and
subsequent breaking of the upper hybrid oscillations at arbitrarily low
amplitudes. This result is in sharp contrast to the usual upper hybrid
oscillations in a homogeneous magnetic field where the oscillations break
within a fraction of a period when the amplitude exceeds a certain critical
value. Our perturbative calculations show that the phase mixing (wave breaking)
time scales inversely with the amplitude of magnetic field inhomogeneity
($\Delta$) and amplitude of imposed density perturbation ($\delta$), and scales
directly with the ratio of magnetic field inhomogeneity scale length to imposed
density perturbation scale length ($(\alpha/k_L)^{-1}$ ) as
$\omega_{pe}\tau_{mix} \sim \left( 1+\beta^2 \right)
^{3/2}k_L/(\beta^2\delta\Delta\alpha)$, where $\beta$ is the ratio of electron
cyclotron frequency to electron plasma frequency. Further phase mixing time
measured in simulations, performed using a 1-1/2 D code based on Dawson sheet
model, shows good agreement with the above mentioned scaling. This result may
be of relevance to plasma based particle acceleration experiments in the
presence of a transverse inhomogeneous magnetic field.
