As the Shulchan Aruch rules (671:7), Chanukah candles are lit each night of Chanukah not only in the home, but in the synagogue, as well, in order to further publicize the miracle. This practice assumes particular importance nowadays, when people generally light Chanukah candles inside the home and thus publicize the miracle only to the other family members. Lighting Chanukah candles in the synagogue achieves a greater degree of Kiddush Hashem (sanctification of God's Name) in publicizing the miracle of Chanukah on a public scale.
Is it necessary for the Chanukah candles lit in the synagogue to burn for a half-hour, as is required for the lighting in the home? Furthermore, must the person lighting the candles ensure to add enough oil or use a long enough candle to sustain a flame for a half-hour period?
As Chacham Ovadia Yosef cites in his work Chazon Ovadia (Laws of Chanukah, p. 46), many authorities held that since the synagogue lighting is performed purely for the sake of publicizing the miracle to the congregation, the candles must burn only while people remain in the synagogue. It is not necessary to ensure that the candles burn for a half-hour, and it suffices to have them burn only so long as people are present in the synagogue. Therefore, one need not provide enough oil or use a long enough candle to sustain a flame for a half-hour, and one may extinguish the candles once the people have left the synagogue.
The Mishna Berura (commentary to the Shulchan Aruch by Rabbi Yisrael Meir Kagan, the "Chafetz Chayim," Lithuania, 1839-1933) indeed mentions that the Chanukah candles lit in the synagogue must burn for the same duration of time as the candles lit at home (673:13). However, Chacham Ovadia Yosef claimed that the Mishna Berura referred only to communities where people remain in the synagogue after Arbit, such as for a Shiur and the like. Generally, however, when the congregation disperses immediately following the Arbit service, the candles need not burn after the people leave the synagogue.
Finally, Chacham Ovadia Yosef rules (Chazon Ovadia, Laws of Chanukah, p. 47) that a Minyan praying Arbit during Chanukah at the Kotel Ha'ma'aravi (Western Wall) in Jerusalem should light Chanukah candles before reciting the Arbit prayer. Since the area of the Kotel is used as a synagogue, Chanukah candles must be kindled at the site with a Beracha just like in ordinary synagogues, in order to publicize the Chanukah miracle.
Summary: The one who kindles the Chanukah candles in the synagogue is not required to provide enough oil or use long enough candles to sustain a flame for a half-hour; it suffices to ensure that the candles burn while long as people remain in the synagogue. Likewise, one may extinguish the candles when people leave the synagogue. A Minyan praying Arbit at the Western Wall in Jerusalem during Chanukah must light Chanukah candles with a Beracha, just as in ordinary synagogues.
