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We investigate the time-dependent behavior of Crab-like pulsar wind nebulae(PWNe) generating a set of models using 4 different initial spin-downluminosities ($L_0 =\{1,0.1,0.01,0.001\} \times L_{0, {\rm Crab}}$), 8 valuesof magnetic fraction ($\eta =$ 0.001, 0.01, 0.03, 0.1, 0.5, 0.9, 0.99, and0.999, i.e., from fully particle dominated to fully magnetically dominatednebulae), and 3 distinctive ages: 940, 3000, and 9000 years. We find that theself-synchrotron Compton (SSC) contribution is irrelevant for $L_{SD}$=0.1, 1,and 10% of the Crab power, disregarding the age and the magnetic fraction. SSConly becomes relevant for highly energetic ($\sim 70%$ of the Crab), particledominated nebulae at low ages (of less than a few kyr), located in a FIRbackground with relatively low energy density. Since no pulsar other than Crabis known to have these features, these results clarify why the Crab Nebula, andonly it, is SSC dominated. No young PWN would be detectable at TeV energies ifthe pulsar's spin-down power is 0.1% Crab or lower. For 1% of the Crabspin-down, only particle dominated nebulae can be detected by H.E.S.S.-liketelescopes when young enough (with details depending on the precise injectionand environmental parameters). Above 10% of the Crab's power, all PWNe aredetectable by H.E.S.S.-like telescopes if they are particle dominated, nomatter the age. The impact of the magnetic fraction on the final SED is variedand important, generating order of magnitude variations in the luminosityoutput for systems that are otherwise the same (equal $P$, $\dot P$, injection,and environment).

The effects of magnetic field, age, and intrinsic luminosity on Crab-like pulsar wind nebulae