Sure! Here’s a Python function to generate test cases for the given competitive programming problem "Accelerated Railgun". This function generates random values for \(D\), \(px\), \(py\), \(vx\), and \(vy\) while adhering to the constraints specified in the problem statement.

```python
import random

def generate_random_value(min_val, max_val, precision):
    return round(random.uniform(min_val, max_val), precision)

def tcgen():
    test_cases = []
    
    while True:
        # Probability of terminating input
        if random.random() < 0.1:
            test_cases.append("0")
            break
            
        # Generate D
        D = generate_random_value(0.0001, 50, 4)
        
        # Generate px, py
        px = generate_random_value(0.0001, 0.9999, 4)
        py = generate_random_value(0.0001, 0.9999, 4)
        
        # Generate vx, vy
        vx = generate_random_value(0.0001, 0.9999, 4)
        vy = generate_random_value(0.0001, 0.9999, 4)
        
        test_cases.append(f"{D}")
        test_cases.append(f"{px} {py} {vx} {vy}")
    
    return "\n".join(test_cases)

# Example usage:
print(tcgen())
```

Explanation:
1. `generate_random_value` function generates a random float between `min_val` and `max_val` with a specified precision.
2. `tcgen` function constructs several test cases until it decides to terminate (randomly decided with a 10% probability for this example).
3. For each test case:
   - `D` is generated within the range [0.0001, 50].
   - \(px\) and \(py\) are generated within the range [0.0001, 0.9999].
   - \(vx\) and \(vy\) are generated within the range [0.0001, 0.9999].
4. The test cases are collected in a list and then joined into a single string with newline characters separating each line.

This function ensures that the generated test cases comply with the given constraints, and they are appropriate for use in testing the "Accelerated Railgun" problem.