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Recent observations have detected extended TeV gamma-ray emission surroundingyoung and middle-aged pulsars. The morphology of these "TeV halos" requirescosmic-ray diffusion to be locally suppressed by a factor of ~100-1000 comparedto the typical interstellar medium. No model currently explains thissuppression. We show that cosmic-ray self-confinement can significantly inhibitdiffusion near pulsars. The steep cosmic-ray gradient generates Alfven wavesthat resonantly scatter the same cosmic-ray population, suppressing diffusionwithin ~20 pc of pulsars younger than ~100 kyr. In this model, TeV halos evolvethrough two phases, a growth phase where Alfven waves are resonantly generatedand cosmic-ray diffusion becomes increasingly suppressed, and a subsequentrelaxation phase where the diffusion coefficient returns to the standardinterstellar value. Intriguingly, cosmic-rays are not strongly confined earlyin the TeV halo evolution, allowing a significant fraction of injected e+e- toescape. If these e+e- also escape from the surrounding supernova remnant, theywould provide a natural explanation for the positron excess observed by PAMELAand AMS-02. Recently created TeV cosmic-rays are confined in the TeV halo,matching observations by HAWC and H.E.S.S. While our default model relaxes toorapidly to explain the confinement of TeV cosmic rays around mature pulsars,such as Geminga, models utilizing a Kraichnan turbulence spectrum experiencemuch slower relaxation. Thus, observations of TeV halos around mature pulsarsmay provide a probe into our understanding of interstellar turbulence.

Self-Generated Cosmic-Ray Confinement in TeV Halos: Implications for TeV Gamma-Ray Emission and the Positron Excess