In tandem mass spectrometry of proteins one will usually end up with a mix of $b$ and $y$ fragments but also $a$ fragments and immonium fragments. My problem is that wouldn't an $a_1$ ion be the exact same as an immonium ion of the first amino acid in the peptide?
I don't know if you are still interested in this question. But yes, the a1 ion would have exact the same m/z as the immonium ion of all amino acids of the same type in the pepitde. Peptides typically fragment in low energy fragmentation methods such as CID by charg-directed mechanisms, which mainly produces y and b series ions. These ions can fragment further to lower b ions, a ions, or internal fragments and immonium ions. y and b ions are much easier to understand and we therefore mostly use these ions for interpretation of mass spectra.