Energy loss at the LHC recent problem

The recent physics problem "Energy loss at the LHC" asks to calculate energy loss by a bunch of protons in LHC due to syncrotron radiation. It is assumed that the radiated energy scales linearly with the number of particles. On the other hand, the power radiated by a single particle $\frac{2ke^2p^4}{3m^4c^3r^2}$ scales quadratically with the particle mass if we increase charge and momentum proportionally. As far as I understand, this quadratic dependence could be accounted for by a coherence of emitted radiation. Wouldn't the power in question also scale quadratically with the number of particles?

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$