Production of the top-pions at the THERA collider based $\gamma p$ collisions

In the framework of the topcolor-assisted technicolor (TC2) models, we study the production of the top-pions ${\pi }_t^0$, ${\pi }_t^{\pm }$ via the processes $ep\to \gamma c\to {\pi }_t^{0}c$ and $ep\to \gamma c\to {\pi }_t^{\pm }b$ mediated by the anomalous top coupling $tc\gamma$. We find that the production cross section of the process $ep\to \gamma c\to {\pi }_t^{0}c$ is very small. With reasonable values of the parameters in TC2 models, the production cross section of the process $ep\to \gamma c\to {\pi }_t^{\pm }b$ can reach $1.2pb$. The charged top-pions ${\pi }_t^{\pm }$ might be directly observed via this process at the THERA collider based $\gamma p$ collisions.