BEIJING, June 29 (Reuters) - Zinc fell back in London and Shanghai on Friday after jumping in the previous session on the prospect of Chinese smelters cutting output by 10 percent in response to lower zinc prices and treatment charges, a key source of revenue. The metal, used to galvanise steel, is on course to shed 11.8 percent in London and 5.3 percent in Shanghai in the second quarter, which in both cases would mark its worst quarter since the third quarter of 2015. LME zinc is also set for a drop of 7 percent in June alone, which would be its steepest monthly drop since November 2015. FUNDAMENTALS * ZINC: Zinc on the London Metal Exchange was down 0.5 percent at $2,882 a tonne as of 0221 GMT, having ended up 0.7 percent on Thursday. The most traded August zinc contract on the Shanghai Futures Exchange (ShFE) edged down 0.04 percent to 23,215 yuan ($3,498.40) a tonne. * COPPER: Three-month copper on the LME was flat at $6,620.50 a tonne and on track for a 1.4 percent dip this quarter. ShFE copper fell by 0.7 percent but is still set for a 1.8 percent gain over the three months. * OTHER METALS: Shanghai nickel is set for its best quarter since the contract was launched in 2015, with a 17.8 percent rise, while lead is poised to add 16.4 percent this quarter amid an environmental crackdown in China. * TC/RCs: China's top copper smelters on Thursday failed to set minimum treatment and refining charges (TC/RCs) for copper concentrate in the third quarter of 2018, two people with knowledge of the matter said. * RUSAL: Shareholders at sanctions-hit Russian aluminium producer Rusal elected a new board of directors on Thursday in an effort to appease the U.S. and get the restrictions lifted. * VALE: Brazilian miner Vale <VALE3.SA< said on Thursday it would pay 557.7 million reais ($144.42 million) in the second half of the year to restore the environment and communities damaged by a 2015 disaster at Samarco, a joint venture it has with BHP Billiton.