simulate the processes with mu- mu+ and mu- A initial states

Hi Zhicheng,
the answer depends a bit on what kind of physics you want to simulate. At the moment, there are not yet beam spectra for the muon collider via CIRCE2 in the same way as for CEPC, ILC, CLIC (and soon FCC-ee). For the moment, the advice from machine physicists is to use a Gaussian beam spread of 0.1%.
The beam statement would then have to read, e.g. for the Higgsstrahlung process:

process mmzh = e2, E2 => Z, H

beams = e2, E2 => gaussian
gaussian_spread1 = 0.1%
gaussian_spread2 = 0.1%

In addition to that you can switch one leading-log (LL) muon PDFs which describe the collinear resummation of all-order soft and up to third-order hard collinear photons. This would then be
beams = e2, E2 => gaussian => isr
gaussian_spread1 = 0.1%
gaussian_spread2 = 0.1%
instead.

For the muon-photon process it depends whether you want photons from the beam spectrum in analogy to the eg and ge components of the ILC and CLIC spectra or collinear QED splittings of e -> e A in the initial state. The first option is not yet available (though work in progress), the second option would be a equivalent photon approximation (EPA), also know as Weizsacker-Williams.

This would work as (e.g. for single-W production)

process mmaw = e2, A => n2, E1, n1
beams = e2, E2 => none, epa
epa_mass = 105.6 MeV
epa_x_min = 0.01

This can be combined with the Gaussian spread, of course,
beams = e2, E2 => gaussian => none, epa
epa_mass = 105.6 MeV
epa_x_min = 0.01

Also, for the electron part, you can still switch on ISR:
beams = e2, E2 => gaussian => isr, epa
[...]

Cheers,
   JRR (Juergen Reuter)