In intense charged particle beams with large energy anisotropy, free energy is available to drive transverse electromagnetic Weibel-type instabilities. Such slow-wave transverse electromagnetic instabilities can be described by the so-called Darwin model, which neglects the fastwave portion of the displacement current. The Weibel instability may also lead to an increase in the longitudinal velocity spread, which would make the focusing of the beam difficult and impose a limit on the minimum spot size achievable in heavy ion fusion experiments. This paper reports the results of recent numerical studies of the Weibel instability using the Beam Eigenmode And Spectra (bEASt) code for space-charge-dominated, low-emittance beams with large tune depression. To study the nonlinear stage of the instability, the Darwin model is being developed and incorporated into the Beam Equilibrium Stability and Transport(BEST) code.
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