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Update EmittanceInvariants.H
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Add literature citations.
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cemitch99 committed Sep 16, 2024
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20 changes: 17 additions & 3 deletions src/particles/diagnostics/EmittanceInvariants.H
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namespace impactx::diagnostics
{

/** Returns the three independent kinetic invariants
/** Returns the three independent kinematic moment invariants
* denoted I2, I4, and I6 as constructed from the 6x6
* beam covariance matrix. These three quantities are invariant
* under any linear symplectic transport map, and are used in the
* calculation of the three eigenemittances.
* calculation of the three eigenemittances, as described in:
*
* G. Rangarajan, F. Neri, and A. Dragt, "Generalized Emittance
* Invariants," in Proc. 1989 IEEE Part. Accel. Conf., Chicago, IL,
* 1989, doi:10.1109/PAC.1989.73422.
* A. Dragt, F. Neri, and G. Rangarajan, "General Moment Invariants
* for Linear Hamiltonian Systems," Phys. Rev. A 45, 2572-2585 (1992),
* doi:10.1103/PhysRevA.45.2572.
*
* @param[in] Sigma symmetric 6x6 covariance matrix
* @returns tuple containing invariants I2, I4, and I6
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* beam covariance matrix. These three quantities are invariant
* under any linear symplectic transport map, and reduce to
* the projected normalized rms emittances in the limit of
* uncoupled transport.
* uncoupled transport. These quantities are described in:
*
* G. Rangarajan, F. Neri, and A. Dragt, "Generalized Emittance
* Invariants," in Proc. 1989 IEEE Part. Accel. Conf., Chicago, IL,
* 1989, doi:10.1109/PAC.1989.73422.
* A. Dragt, F. Neri, and G. Rangarajan, "General Moment Invariants
* for Linear Hamiltonian Systems," Phys. Rev. A 45, 2572-2585 (1992),
* doi:10.1103/PhysRevA.45.2572.
*
* @param[in] Sigma symmetric 6x6 covariance matrix
* @returns tuple containing eigenemittances e1, e2, and e3
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