What is the test for a judge to participate in a trial?

A trial judge must avoid the appearance of advocacy or partiality. See United States v. Eldred, 588 F.2d 746, 749 (9th Cir.1978) (per curiam). A judge "may participate in the examination of witnesses to clarify evidence, confine counsel to evidentiary rulings, ensure the orderly presentation of evidence, and prevent undue repetition." United States v. Laurins, 857 F.2d 529, 537 (9th Cir.1988), cert. denied, 492 U.S. 906 (1989). "A judge's participation justifies a new trial only if the record shows actual bias or leaves an abiding impression that the jury perceived an appearance of advocacy or partiality." Id.