Page 16 - Progress minimizing fast-ion charge-exchange loss associated with gas injection on C-2W
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Complications to Effective Potentials
• Introducing a non-axisymmetric perturbation disrupts the notion of Ueff, which inherently relies on !" = 0 in an axisymmetric field
• Since that condition is no longer satisfied, Pθ is no longer conserved and Ueff is not a well- defined quantity
• However, we can restrict ourselves to a mode with a narrow radial extent, such that: Δ𝑟$%&' < 𝜌(
• If that holds, we can then assume the particle, when outside the perturbed region, is confined in a “temporary” Ueff which undergoes some change at each passing through the mode region:
𝑃# 𝑡) =𝑃# 𝑡* +𝛿𝑃#
𝑈'++𝑡) ≈𝑈'++𝑡* −𝑞𝜓𝛿𝑃#+𝑂 𝛿𝑃#, 𝑚𝑟,
!#
Presenter: Gabriel Player
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