A student pilot departing from a sea level airport suffered a loss of power shortly after takeoff. During the magneto check the engine had been leaned to best power mixture but not returned to full rich prior to takeoff.

Narrative

As part of my Part 141 training program I was preparing a solo cross-country flight from ZZZ to ZZZ2 and back. My flight plan and navigation log was reviewed and signed off by my instructor. I contacted Flight Service by telephone and after submitting my flight plan I asked for a standard weather briefing and NOTAMs; which I duly received and made note of. After review with my instructor of all endorsements; other Part 141 documents and my medical certificate; I completed all items on the preflight checklist. The engine started normally and I proceeded to the run-up area. After continuation of the checklist I started setting up the magneto check. I increased the engine RPM to 1800 RPM and did not set the mixture to full rich. Instead I leaned the mixture according to the instructor's alternative procedure (alternative procedure being; lean mixture resulting in increase of engine RPM until visual RPM drop; then re-enrich mixture until max RPM achieved before the drop). With the mixture set; I performed a satisfactory magneto check within the boundaries of the checklist. During the leaning prior to and during the magneto check I noticed some engine roughness but was not worried at the time as I believed this to be minor and it subsequently subsided. After having received clearance to Runway 4R at Foxtrot via Charley; I taxied to the said position and held short at the active runway. I was then cleared for takeoff from Runway 4R. Deviating from the checklist; I did not set mixture to FULL rich but maintained the optimized leaned out setting (as per prior instructions from instructors regarding takeoffs). I rolled onto the runway; added full power and took off slightly above 55 KTS; all engine systems and indications in the green. A few moments after being airborne - perhaps at 150-300 FT - the engine displayed extreme roughness and a significant loss of power. As I knew I could not turn below 500 FT I had to land in a straight line back onto the departing Runway 4R. I did not hesitate and pulled back power immediately preparing for an emergency landing. While reducing power to almost idle; I contacted the Tower; explained I had engine issues/failure and requested immediate landing back on Runway 4R. The Tower cleared me for landing and asked if I need further assistance. I declined further assistance and landed at the far end of Runway 4R close to the end of the runway. The Tower asked if everything was alright and requested my intentions. I stated that all was well and as the engine was still running I requested taxi back to the FBO. At the parking area I completed the post-landing checklist and walked back to the FBO. I contacted my instructor immediately and informed her of the events in person as she was on the premises. There were no injuries or property damage to anyone or anything. I only spent the previous 3 lessons in this aircraft. My regular plane was down for maintenance.