A catheter includes at least one electrode provided at its distal end. A spacing structure, provided at the catheters distal end and encompassing the electrode, is transformable between a low-profile introduction configuration and a larger-profile deployed configuration, and maintains space between the electrode and a wall of a renal artery when electrical energy sufficient to ablate perivascular renal nerve tissue adjacent the renal artery is delivered by the electrode. The spacing structure may comprise perforations allowing for passage of arterial blood therethrough and transport of high frequency alternating current from the electrode to the perivascular renal nerve tissue via the blood, with no or negligible thermal injury to the artery wall. An ablation catheter with an electrode encompassed spacing structure can be deployed in each renal artery to deliver bipolar RF energy for ablating perivascular renal nerve tissue and ganglia near the aortorenal junctions.