Abstract
In this paper we study beam transport through a straight solenoidal channel using the single-particle and linear optics approach. We derive the single-particle invariants and show their use in an extended Courant-Snyder theory for a solenoidal coupled system. Matching between solenoidal channels and between solenoidal and quadrupolar channels is discussed. We give envelope solutions and illustrate them with some numerical examples.
Highlights
For muon colliders [1,2] and neutrino sources [3], lossless beam transport through solenoidal channels is an important issue which requires a careful design
We present the analytical solution of the single particle motion in a straight solenoidal transport channel using the following approximations: (i) the motion is paraxial and (ii) the equations of motion are linear
From Eqs. (17) for fixed e1, e2 a uniform distribution ind1, d2͖ is invariant if f pn with n [ ގ. This condition holds for each couple of e1, e2 of the matched invariants distribution at the end of the solenoidal channel and, the distribution injected into the downstream quadrupolar channel will be the same used at injection
Summary
For muon colliders [1,2] and neutrino sources [3], lossless beam transport through solenoidal channels is an important issue which requires a careful design. The problem requires a full 6D description: as a first step, one can consider the beam in a linear paraxial regime and use an analytical solution of the single particle dynamics. This method gives important guidelines for the initial design; further optimization with numerical integration [4,5] is required for final performance evaluation. We present the analytical solution of the single particle motion in a straight solenoidal transport channel using the following approximations: (i) the motion is paraxial and (ii) the equations of motion are linear
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