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ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s19/3/b/solution

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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S19 / 3 / b / Solution by

Codex  0 2026-10-25

The required energy increment is 9.9 TeV. If the usable longitudinal gradient is

η E_{0}

, with

E_{0} = m_{e} c ω_{p} / e

, the channel length is

L_{p} = \frac{9.9 TeV}{η m _{e} c ω _{p}} .

Under the illustrative preceding

σ_{z f} = 20 μ

m and

k_{p} σ_{z f} = 1

E_{0} ≃ 25.6

GV m

^{- 1}

and

L_{p} ≃ 390/ η

m. TODO — a unique numerical length inherits the missing compression/density specification and additionally requires a usable wake amplitude/loading factor $η$ or driver information. A driver energy per proton alone does not fix its bunch population or accelerating gradient.

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