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Following discharge from a Hall effect thruster, charge exchange occurs between ions and un-ionized propellant atoms. The low-energy cations produced can disturb operation of onboard instrumentation or the thruster itself. Charge-exchange cross sections for both singly and doubly charged propellant atoms are required to model these interactions. While xenon is the most common propellant currently used in Hall effect thrusters, other propellants are being considered, in particular, krypton. We present here guided-ion beam measurements and comparisons to semiclassical calculations for Kr+ + Kr and Kr2+ + Kr cross sections. The measurements of symmetric Kr+ + Kr charge exchange are in good agreement with both the calculations including spin-orbit effects and previous measurements. For the symmetric Kr2+ + Kr reaction, we present cross section measurements for center-of-mass energies between 1 eV and 300 eV, which spans energies not previously examined experimentally. These cross section measurements compare well with a simple one-electron transfer model. Finally, cross sections for the asymmetric Kr2+ + Kr → Kr+ + Kr+ reaction show an onset near 12 eV, reaching cross sections near constant value of 1.6 Å2 with an exception near 70–80 eV.