A laptop can be charged without its original power adapter. However, there is no safe way to charge it without a replacement adapter or another charging device.
Although the best adapter is one made specifically for a particular device, the simplest solution may be to purchase a universal adapter, which works with any device compatible with the jack, amperage and voltage. Universal adapters are widely available at electronics retailers.
Portable charging devices include solar units that rely on the sun to recharge devices. Other portable chargers and battery backups must be charged or plugged into an outlet and then attached to the laptop.