Active Current Limiter
The simplest way to create a constant current is to use the inherent current regulating characteristic of a bipolar transistor. If you feed a fixed current into the Base, current at the Collector will be multiplied by the transistor's current gain (&beta; or HFE), which is relatively constant over a wide range of Collector-Emitter voltages. The circuit is very simple:-







simulate this circuit &ndash; Schematic created using CircuitLab

R1 sets Q1's Base current to 1mA. Q1 has HFE of about 100, so ~100mA flows from Emitter to Collector to charge the capacitor. 

Unfortunately there is a catch:- current gain is a difficult parameter to control in manufacture. So while 100 is the 'typical' figure, an individual transistor might be &lt;50 or >150 - and affected quite strongly by temperature. You can adjust R1 to suit an individual transistor, and use a good heatsink to keep the temperature stable, but you can't expect the current to stay at exactly 100mA.       

If you don't need an exact charging current and are willing to 'tune' it to suit the individual transistor then this simple circuit may be enough for you. 

But if you want better accuracy and stability then you need a circuit which measures the current and compares it to a stable reference, turning the transistor on more or less to keep the current constant. This technique does not rely on HFE so it can use a bipolar transistor or a FET. Here's an example circuit:-







simulate this circuit

R1 and R2 provide a reference voltage of 100mV (relative to 28V) when the potentiometer is centered (variable from 0 to 200mV to adjust the output current). R5 senses the output current by dropping a voltage of 1V per Amp. Op amp OA1 compares these two voltages, and varies Q1's Base current (via R4) until they match.

Because the sense resistor must drop some voltage to measure the output current, this circuit has a slightly lower maximum output voltage than the simple transistor regulator. However it is much more accurate, and not sensitive to the characteristics of the transistor.