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By means of mean-field theory, we have studied the structure and excitationspectrum of a purely dipolar Bose gas in pancake-shaped trap where theconfinement in the x-y plane is provided by a highly anharmonic potentialresulting in an almost uniform confinement in the plane. We show that thestable condensates is characterized by marked radially structured densityprofiles. The stability diagram is calculated by independently varying thestrength of the interaction and the trap geometry. By computing the Bogoliubovexcitation spectrum near the instability line we show that soft "angular"rotons are responsible for the collapse of the system. The free expansion ofthe cloud after the trap is released is also studied by means of time-dependentcalculations, showing that a prolate, cigar-shaped condensate is dynamicallystabilized during the expansion, which would otherwise collapse. Dipolarcondensates rotating with sufficiently high angular velocity show the formationof multiply-quantized giant vortices, while the condensates acquire aring-shaped form.

Dipolar Bose gas in highly anharmonic traps