The Low Geminga Halo Diffusion Coefficient and a Gradient Driven Alfven Instability

Detailed observation by the High-Altitude Water Cerenkov Observatory of the regions within about 20 pc of the nearby Geminga and PSR B0656+14 pulsars have suggested the need for the diffusion coefficient of 10-100 TeV leptons yielding the detected gamma-rays to be about 4x10^27 cm^2 s^-1, two orders of magnitude less than the value usually required to explain galactic cosmic ray propagation at these energies. This result casts doubt on the ability of pulsars to explain the positron excess above the value determined by secondary cosmic ray production, although use of two zone diffusion models mitigates the problem. It is the purpose of this paper to give a simple demonstration of the possibility that the gradient in the pulsar accelerated electrons/positrons can give rise to the Alfven instability whereby the particles are self-confined. An estimated value of the Halo diffusion coefficient of 3x10^27 cm^2 s^-1 at 47 TeV is found.