Turing machine that accepts $L = {a^n^2 | n ≥ 1 }$

I have the following language:

$ L = \{a^{n^2} | n ≥ 1 \}$

I am trying to construct a Turing machine that accepts L. My basic idea (without success) is to use a 2-tape TM where in the 2-tape compute the string with length $ n^2$ . After that, I wish to compare the length of the input string in the 1-tape with the length of the string on the 2-tape.