Page 15 - Progress minimizing fast-ion charge-exchange loss associated with gas injection on C-2W

Forbidden Orbits in FRCs
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𝑃# and E are not totally independent variables, since there is a mechanical component of P that depends on the particle energy
Briefly, we can define the velocity:
𝑣%= 2𝐸 ;𝛼=tan&' 𝑣# 𝑚 1 + tan$ 𝛼 𝑣%
𝑣# =𝑣%tan 𝛼 = 2𝐸 tan 𝛼 ;𝜆( =1+tan$ 𝛼 𝑚𝜆(
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Which allows us to re-define 𝑃#:
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Which clearly has minimum and maximum allowed values for a given energy (defined for 𝛼 = 90° , −90°)
𝑃# = 𝑚𝑟𝑣# + 𝑞𝜓 𝑟
𝑃#= 2𝑚𝑟$tan𝛼 ∗ 𝐸+𝑞𝜓𝑟 𝜆(
Presenter: Gabriel Player
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