Why do cations have higher ionization energies than neutral atoms?
Consider a simple thought experiment. Your ionisation process is essentially removing a (negatively charged) electron from a remainderatom.

$$\ce{Atom^n+ -&gt; Remainderatom^{(n+1)+} + e-}$$

Throughout this process, you are separating charges, thus there is an electrostatic force driving the electron back to its remainderatom.

If the remainderatom has a charge of $2\ (\Rightarrow n=1)$, the attractive force is twice as strong in simplistic theories than if remainderatom’s charge is $1\ (\Rightarrow n=0)$.

Thus, it is twice as hard to remove a second electron.



This thought experiment makes use of a number of simplifications. For example, it does not consider electron energy levels (orbitals), it does not consider orbital contraction upon ionisation and much more. But it does a good job at explaining the general trend.