Always lowercase.
The federal court system that exists today as the outgrowth of Article 3 of the Constitution is composed of the Supreme Court of the United States, the U.S. Court of Appeals, U.S. District Courts, and the U.S. Customs Court. There are also four district judges for U.S. territories.
U.S. bankruptcy and magistrate judges are fixed-term judges serving in U.S. District Courts. Magistrate judges are generalist judges who preside in cases referred from U.S. district judges. Bankruptcy judges are specialized judges whose authority is restricted to bankruptcy issues.
The U.S. Tax Court and the U.S. Court of Military Appeals for the Armed Forces are not part of the judicial branch as such.