Construct Turing Machine which accepts the language $ww$

I try to construct a TM that accepts the language $\{ ww \mid w \in \{a,b\}^* \}$.

Between the words $w$ is no delimeter, so I don't know, how my TM can know where the first $w$ ends and the second $w$ begins.

Is there a trick for this?

Here is a sketch for how a deterministic machine might work:

• place a marker in front of the input.

• go through the input, checking if the length is even. If not, reject.

• place a marker behind the input.

• going back and forth, move the markers towards each other until they meet in the middle.

• as long as the halves are nonempty, compare and erase their first letters and reject if not equal.

• accept.

StackExchange Computer Science Q#43639, answer score: 5