LED's are funny things. They only work at Vdc within specific tolerances, and normally connected with a current limiting resistor to the powersource. Instead of a resistor, you can use a FET (Field Effect Transistor) such as the ECG312, NTE312 which are good for up to 30Vdc max. The MPF102 will also work just fine, just the max voltage is 25V. Other types will also work, just watch the maximum rated voltage versus your input voltage. They easily blow if the you go above the maximum specifications. Keep in mind that, although the circuit works as shown, it is not protected against voltage spikes. You can add that feature yourself if needed. I actually strongly recommend it.
When the gate and the source are connected together, it behaves as a current regulator. In the circuit above the current is constant between 6 and 8 mA at 5 to 30Vdc. Because of the set current of around 6mA the older LED's will glow faintly at best. I'm talking about the led types from the 70's wich are still kicking around.
And another tip, try to get the results you want with a variable powersupply and start with about 5volts or so. It may save a couple types of J-Fets from early retirement... :-)
If a diode is added such as a 1N4148 or similar, it can be connected to a AC source of 5 to 20 V-AC (NTE312).
I found that the 3mm type led's work best, but I give the green leds preference.
In addition, the BF types can be used. Select the type according to current use.